{"id":9546,"date":"2023-06-19T01:54:32","date_gmt":"2023-06-18T23:54:32","guid":{"rendered":"https:\/\/www.maximebaczyk.fr\/?page_id=9546"},"modified":"2023-11-24T23:01:23","modified_gmt":"2023-11-24T22:01:23","slug":"theorie-phenomenes-critiques","status":"publish","type":"page","link":"https:\/\/www.maximebaczyk.fr\/?page_id=9546","title":{"rendered":"Ph\u00e9nom\u00e8nes critiques"},"content":{"rendered":"<div data-colibri-id=\"9546-c1\" class=\"style-1671 style-local-9546-c1 position-relative\">\n  <!---->\n  <div data-colibri-component=\"section\" data-colibri-id=\"9546-c2\" id=\"custom\" class=\"h-section h-section-global-spacing d-flex align-items-lg-center align-items-md-center align-items-center style-1672 style-local-9546-c2 position-relative\">\n    <!---->\n    <!---->\n    <div class=\"h-separator\" style=\"height: 100px; bottom: calc(0px);\">\n      <svg style=\"fill:rgb(12, 12, 12);transform:rotateX(180deg);\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" viewBox=\"0 0 1000 20\" preserveAspectRatio=\"none\">\n        <path class=\"svg-white-bg\" d=\"M0,0v3c0,0,393.8,0,483.4,0c9.2,0,16.6,7.4,16.6,16.6c0-9.1,7.4-16.6,16.6-16.6C606.2,3,1000,3,1000,3V0H0z\"><\/path>\n      <\/svg>\n    <\/div>\n    <div class=\"h-section-grid-container h-section-boxed-container\">\n      <!---->\n      <div data-colibri-id=\"9546-c3\" class=\"h-row-container gutters-row-lg-2 gutters-row-md-2 gutters-row-0 gutters-row-v-lg-2 gutters-row-v-md-2 gutters-row-v-2 style-1753 style-local-9546-c3 position-relative\">\n        <!---->\n        <div class=\"h-row justify-content-lg-center justify-content-md-center justify-content-center align-items-lg-stretch align-items-md-stretch align-items-stretch gutters-col-lg-2 gutters-col-md-2 gutters-col-0 gutters-col-v-lg-2 gutters-col-v-md-2 gutters-col-v-2\">\n          <!---->\n          <div class=\"h-column h-column-container d-flex h-col-lg-auto h-col-md-auto h-col-auto style-1754-outer style-local-9546-c4-outer\">\n            <div data-colibri-id=\"9546-c4\" class=\"d-flex h-flex-basis h-column__inner h-px-lg-2 h-px-md-2 h-px-2 v-inner-lg-2 v-inner-md-2 v-inner-2 style-1754 style-local-9546-c4 position-relative\">\n              <!---->\n              <!---->\n              <div class=\"w-100 h-y-container h-column__content h-column__v-align flex-basis-100 align-self-lg-start align-self-md-start align-self-start\">\n                <!---->\n                <div data-colibri-id=\"9546-c5\" class=\"h-text h-text-component style-1756 style-local-9546-c5 position-relative h-element\">\n                  <!---->\n                  <!---->\n                  <div class=\"\">\n                    <p><em style=\"font-family: &quot;Playfair Display&quot;; color: rgb(6, 6, 6); font-size: 100%;\">Ces notes constituent une introduction au mod\u00e8le d&rsquo;Ising ainsi qu&rsquo;\u00e0 ses applications en physique statistique, surtout centr\u00e9es autour de la th\u00e9orie des transitions de phases et des ph\u00e9nom\u00e8nes critiques.<\/em><\/p>\n                    <p><em style=\"font-family: &quot;Playfair Display&quot;; color: rgb(6, 6, 6); font-size: 100%;\"> Une transition de phases dans un syst\u00e8me macroscopique, c&rsquo;est \u00e0 dire constitu\u00e9 par un nombre gigantesque d&rsquo;atomes, correspond \u00e0 un changement radical de l&rsquo;\u00e9tat du syst\u00e8me lorsqu&rsquo;on varie l\u00e9g\u00e8rement et continument un param\u00e8tre ext\u00e9rieur. Une telle transition d\u00e9limite ainsi deux phases thermodynamiques accessibles pour le syst\u00e8me aux propri\u00e9t\u00e9s physiques bien diff\u00e9rentes. Les ph\u00e9nom\u00e8nes critiques s&rsquo;identifient \u00e0 une certaine classe de transitions de phases que l&rsquo;on appelle aussi les transitions continues.<\/em><\/p>\n                    <p><span style=\"font-family: Prata; color: rgb(6, 6, 6); font-size: 100%;\"> <\/span><em style=\"font-family: &quot;Playfair Display&quot;; color: rgb(6, 6, 6); font-size: 100%;\">Le mod\u00e8le d&rsquo;Ising, introduit historiquement pour comprendre les transitions de phases, est un mod\u00e8le fondamental de physique statistique qui peut facilement \u00eatre g\u00e9n\u00e9ralis\u00e9 afin d&rsquo;\u00e9tudier des situations physique int\u00e9ressantes et de tenter de r\u00e9pondre \u00e0 des questions encore d\u00e9battues de nos jours.<\/em><\/p>\n                  <\/div>\n                <\/div>\n              <\/div>\n            <\/div>\n          <\/div>\n        <\/div>\n      <\/div>\n      <div data-colibri-id=\"9546-c6\" class=\"h-row-container gutters-row-lg-2 gutters-row-md-2 gutters-row-0 gutters-row-v-lg-2 gutters-row-v-md-2 gutters-row-v-2 style-1675 style-local-9546-c6 position-relative\">\n        <!---->\n        <div class=\"h-row justify-content-lg-center justify-content-md-center justify-content-center align-items-lg-stretch align-items-md-stretch align-items-stretch gutters-col-lg-2 gutters-col-md-2 gutters-col-0 gutters-col-v-lg-2 gutters-col-v-md-2 gutters-col-v-2\">\n          <!---->\n          <div class=\"h-column h-column-container d-flex h-col-lg-auto h-col-md-auto h-col-auto style-1676-outer style-local-9546-c7-outer\">\n            <div data-colibri-id=\"9546-c7\" class=\"d-flex h-flex-basis h-column__inner h-px-lg-2 h-px-md-2 h-px-2 v-inner-lg-2 v-inner-md-2 v-inner-2 style-1676 style-local-9546-c7 position-relative\">\n              <!---->\n              <!---->\n              <div class=\"w-100 h-y-container h-column__content h-column__v-align flex-basis-100 align-self-lg-start align-self-md-start align-self-start\">\n                <!---->\n                <div data-colibri-id=\"9546-c8\" class=\"h-text h-text-component style-1678 style-local-9546-c8 position-relative h-element\">\n                  <!---->\n                  <!---->\n                  <div class=\"\">\n                    <p><span style=\"font-family: Orbitron; color: rgb(9, 9, 9); font-weight: 500;\">Notes de Cours sur le Mod\u00e8le d&rsquo;Ising et les Ph\u00e9nom\u00e8nes Critiques<\/span><\/p>\n                  <\/div>\n                <\/div>\n              <\/div>\n            <\/div>\n          <\/div>\n        <\/div>\n      <\/div>\n      <div data-colibri-id=\"9546-c9\" class=\"h-row-container gutters-row-lg-2 gutters-row-md-2 gutters-row-0 gutters-row-v-lg-2 gutters-row-v-md-2 gutters-row-v-2 style-1805 style-local-9546-c9 position-relative\">\n        <!---->\n        <div class=\"h-row justify-content-lg-center justify-content-md-center justify-content-center align-items-lg-stretch align-items-md-stretch align-items-stretch gutters-col-lg-2 gutters-col-md-2 gutters-col-0 gutters-col-v-lg-2 gutters-col-v-md-2 gutters-col-v-2\">\n          <!---->\n          <div class=\"h-column h-column-container d-flex h-col-lg-auto h-col-md-auto h-col-auto style-1806-outer style-local-9546-c10-outer\">\n            <div data-colibri-id=\"9546-c10\" class=\"d-flex h-flex-basis h-column__inner h-px-lg-2 h-px-md-2 h-px-2 v-inner-lg-2 v-inner-md-2 v-inner-2 style-1806 style-local-9546-c10 position-relative\">\n              <!---->\n              <!---->\n              <div class=\"w-100 h-y-container h-column__content h-column__v-align flex-basis-100 align-self-lg-start align-self-md-start align-self-start\">\n                <!---->\n                <div data-colibri-id=\"9546-c11\" class=\"icon-list d-flex justify-content-lg-center justify-content-md-center justify-content-center style-1808 style-local-9546-c11 position-relative h-element\">\n                  <!---->\n                  <ul class=\"ul-list-icon vertical-on-desktop vertical-on-tablet vertical-on-mobile justify-content-lg-center justify-content-md-center justify-content-center\">\n                    <!---->\n                    <li class=\"list-item no-gutters\">\n                      <!---->\n                      <div class=\"list-container-divider d-flex justify-content-lg-center justify-content-md-center justify-content-center first-el-spacer\"><\/div>\n                      <a href=\"https:\/\/www.maximebaczyk.fr\/wp-content\/uploads\/2023\/11\/Ising1.pdf\" target=\"_blank\" h-use-smooth-scroll=\"true\" class=\"item-link no-gutters\" rel=\"noopener\">\n                        <div class=\"d-flex h-col no-gutters align-items-lg-center align-items-md-center align-items-center list-item-text-wrapper\">\n                          <div class=\"d-flex\"><span class=\"h-svg-icon style-1808-icon style-local-9546-c11-icon\"><!--Icon by Font Awesome (https:\/\/fontawesome.com)-->\n    <svg version=\"1.1\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" id=\"arrow-circle-right\" viewBox=\"0 0 1536 1896.0833\">\n      <path d=\"M1285 896q0-27-18-45l-91-91-362-362q-18-18-45-18t-45 18l-91 91q-18 18-18 45t18 45l189 189H320q-26 0-45 19t-19 45v128q0 26 19 45t45 19h502l-189 189q-19 19-19 45t19 45l91 91q18 18 45 18t45-18l362-362 91-91q18-18 18-45zm251 0q0 209-103 385.5T1153.5 1561 768 1664t-385.5-103T103 1281.5 0 896t103-385.5T382.5 231 768 128t385.5 103T1433 510.5 1536 896z\"><\/path>\n    <\/svg><\/span><\/div> <span class=\"list-text d-block\"><span>Introduction<\/span><\/span>\n                        <\/div>\n                      <\/a>\n                      <div class=\"list-container-divider d-flex justify-content-lg-center justify-content-md-center justify-content-center\">\n                        <div class=\"list-divider\"><\/div>\n                      <\/div>\n                    <\/li>\n                    <li class=\"list-item no-gutters\">\n                      <!---->\n                      <!---->\n                      <a href=\"https:\/\/www.maximebaczyk.fr\/wp-content\/uploads\/2023\/11\/Ising2.pdf\" target=\"_blank\" h-use-smooth-scroll=\"true\" class=\"item-link no-gutters\" rel=\"noopener\">\n                        <div class=\"d-flex h-col no-gutters align-items-lg-center align-items-md-center align-items-center list-item-text-wrapper\">\n                          <div class=\"d-flex\"><span class=\"h-svg-icon style-1808-icon style-local-9546-c11-icon\"><!--Icon by Font Awesome (https:\/\/fontawesome.com)-->\n    <svg version=\"1.1\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" id=\"arrow-circle-right\" viewBox=\"0 0 1536 1896.0833\">\n      <path d=\"M1285 896q0-27-18-45l-91-91-362-362q-18-18-45-18t-45 18l-91 91q-18 18-18 45t18 45l189 189H320q-26 0-45 19t-19 45v128q0 26 19 45t45 19h502l-189 189q-19 19-19 45t19 45l91 91q18 18 45 18t45-18l362-362 91-91q18-18 18-45zm251 0q0 209-103 385.5T1153.5 1561 768 1664t-385.5-103T103 1281.5 0 896t103-385.5T382.5 231 768 128t385.5 103T1433 510.5 1536 896z\"><\/path>\n    <\/svg><\/span><\/div> <span class=\"list-text d-block\"><span>Spins d&rsquo;Ising et configurations<\/span><\/span>\n                        <\/div>\n                      <\/a>\n                      <div class=\"list-container-divider d-flex justify-content-lg-center justify-content-md-center justify-content-center\">\n                        <div class=\"list-divider\"><\/div>\n                      <\/div>\n                    <\/li>\n                    <li class=\"list-item no-gutters\">\n                      <!---->\n                      <!---->\n                      <a href=\"https:\/\/www.maximebaczyk.fr\/wp-content\/uploads\/2023\/11\/Ising3.pdf\" target=\"_blank\" h-use-smooth-scroll=\"true\" class=\"item-link no-gutters\" rel=\"noopener\">\n                        <div class=\"d-flex h-col no-gutters align-items-lg-center align-items-md-center align-items-center list-item-text-wrapper\">\n                          <div class=\"d-flex\"><span class=\"h-svg-icon style-1808-icon style-local-9546-c11-icon\"><!--Icon by Font Awesome (https:\/\/fontawesome.com)-->\n    <svg version=\"1.1\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" id=\"arrow-circle-right\" viewBox=\"0 0 1536 1896.0833\">\n      <path d=\"M1285 896q0-27-18-45l-91-91-362-362q-18-18-45-18t-45 18l-91 91q-18 18-18 45t18 45l189 189H320q-26 0-45 19t-19 45v128q0 26 19 45t45 19h502l-189 189q-19 19-19 45t19 45l91 91q18 18 45 18t45-18l362-362 91-91q18-18 18-45zm251 0q0 209-103 385.5T1153.5 1561 768 1664t-385.5-103T103 1281.5 0 896t103-385.5T382.5 231 768 128t385.5 103T1433 510.5 1536 896z\"><\/path>\n    <\/svg><\/span><\/div> <span class=\"list-text d-block\"><span>Hamiltonien du mod\u00e8le<\/span><\/span>\n                        <\/div>\n                      <\/a>\n                      <div class=\"list-container-divider d-flex justify-content-lg-center justify-content-md-center justify-content-center\">\n                        <div class=\"list-divider\"><\/div>\n                      <\/div>\n                    <\/li>\n                    <li class=\"list-item no-gutters\">\n                      <!---->\n                      <!---->\n                      <a href=\"https:\/\/www.maximebaczyk.fr\/wp-content\/uploads\/2023\/11\/Ising4.pdf\" target=\"_blank\" h-use-smooth-scroll=\"true\" class=\"item-link no-gutters\" rel=\"noopener\">\n                        <div class=\"d-flex h-col no-gutters align-items-lg-center align-items-md-center align-items-center list-item-text-wrapper\">\n                          <div class=\"d-flex\"><span class=\"h-svg-icon style-1808-icon style-local-9546-c11-icon\"><!--Icon by Font Awesome (https:\/\/fontawesome.com)-->\n    <svg version=\"1.1\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" id=\"arrow-circle-right\" viewBox=\"0 0 1536 1896.0833\">\n      <path d=\"M1285 896q0-27-18-45l-91-91-362-362q-18-18-45-18t-45 18l-91 91q-18 18-18 45t18 45l189 189H320q-26 0-45 19t-19 45v128q0 26 19 45t45 19h502l-189 189q-19 19-19 45t19 45l91 91q18 18 45 18t45-18l362-362 91-91q18-18 18-45zm251 0q0 209-103 385.5T1153.5 1561 768 1664t-385.5-103T103 1281.5 0 896t103-385.5T382.5 231 768 128t385.5 103T1433 510.5 1536 896z\"><\/path>\n    <\/svg><\/span><\/div> <span class=\"list-text d-block\"><span>Sym\u00e9tries et g\u00e9n\u00e9ralisations<\/span><\/span>\n                        <\/div>\n                      <\/a>\n                      <div class=\"list-container-divider d-flex justify-content-lg-center justify-content-md-center justify-content-center\">\n                        <div class=\"list-divider\"><\/div>\n                      <\/div>\n                    <\/li>\n                    <li class=\"list-item no-gutters\">\n                      <!---->\n                      <!---->\n                      <a href=\"https:\/\/www.maximebaczyk.fr\/wp-content\/uploads\/2023\/11\/Ising5.pdf\" target=\"_blank\" h-use-smooth-scroll=\"true\" class=\"item-link no-gutters\" rel=\"noopener\">\n                        <div class=\"d-flex h-col no-gutters align-items-lg-center align-items-md-center align-items-center list-item-text-wrapper\">\n                          <div class=\"d-flex\"><span class=\"h-svg-icon style-1808-icon style-local-9546-c11-icon\"><!--Icon by Font Awesome (https:\/\/fontawesome.com)-->\n    <svg version=\"1.1\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" id=\"arrow-circle-right\" viewBox=\"0 0 1536 1896.0833\">\n      <path d=\"M1285 896q0-27-18-45l-91-91-362-362q-18-18-45-18t-45 18l-91 91q-18 18-18 45t18 45l189 189H320q-26 0-45 19t-19 45v128q0 26 19 45t45 19h502l-189 189q-19 19-19 45t19 45l91 91q18 18 45 18t45-18l362-362 91-91q18-18 18-45zm251 0q0 209-103 385.5T1153.5 1561 768 1664t-385.5-103T103 1281.5 0 896t103-385.5T382.5 231 768 128t385.5 103T1433 510.5 1536 896z\"><\/path>\n    <\/svg><\/span><\/div> <span class=\"list-text d-block\"><span>Equilibre \u00e0 temp\u00e9rature finie<\/span><\/span>\n                        <\/div>\n                      <\/a>\n                      <div class=\"list-container-divider d-flex justify-content-lg-center justify-content-md-center justify-content-center\">\n                        <div class=\"list-divider\"><\/div>\n                      <\/div>\n                    <\/li>\n                    <li class=\"list-item no-gutters\">\n                      <!---->\n                      <!---->\n                      <a href=\"https:\/\/www.maximebaczyk.fr\/wp-content\/uploads\/2023\/11\/Ising6.pdf\" target=\"_blank\" h-use-smooth-scroll=\"true\" class=\"item-link no-gutters\" rel=\"noopener\">\n                        <div class=\"d-flex h-col no-gutters align-items-lg-center align-items-md-center align-items-center list-item-text-wrapper\">\n                          <div class=\"d-flex\"><span class=\"h-svg-icon style-1808-icon style-local-9546-c11-icon\"><!--Icon by Font Awesome (https:\/\/fontawesome.com)-->\n    <svg version=\"1.1\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\" id=\"arrow-circle-right\" viewBox=\"0 0 1536 1896.0833\">\n      <path d=\"M1285 896q0-27-18-45l-91-91-362-362q-18-18-45-18t-45 18l-91 91q-18 18-18 45t18 45l189 189H320q-26 0-45 19t-19 45v128q0 26 19 45t45 19h502l-189 189q-19 19-19 45t19 45l91 91q18 18 45 18t45-18l362-362 91-91q18-18 18-45zm251 0q0 209-103 385.5T1153.5 1561 768 1664t-385.5-103T103 1281.5 0 896t103-385.5T382.5 231 768 128t385.5 103T1433 510.5 1536 896z\"><\/path>\n    <\/svg><\/span><\/div> <span class=\"list-text d-block\"><span>Fondements th\u00e9oriques et preuves<\/span><\/span>\n                        <\/div>\n                      <\/a>\n                      <div class=\"list-container-divider d-flex justify-content-lg-center justify-content-md-center justify-content-center\" style=\"display: none;\">\n                        <div class=\"list-divider\"><\/div>\n                      <\/div>\n                      <div class=\"list-container-divider d-flex justify-content-lg-center justify-content-md-center justify-content-center last-el-spacer\"><\/div>\n                    <\/li>\n                  <\/ul>\n                <\/div>\n              <\/div>\n            <\/div>\n          <\/div>\n        <\/div>\n      <\/div>\n      <div data-colibri-id=\"9546-c12\" class=\"h-row-container gutters-row-lg-2 gutters-row-md-2 gutters-row-0 gutters-row-v-lg-2 gutters-row-v-md-2 gutters-row-v-2 style-1826 style-local-9546-c12 position-relative\">\n        <!---->\n        <div class=\"h-row justify-content-lg-center justify-content-md-center justify-content-center align-items-lg-stretch align-items-md-stretch align-items-stretch gutters-col-lg-2 gutters-col-md-2 gutters-col-0 gutters-col-v-lg-2 gutters-col-v-md-2 gutters-col-v-2\">\n          <!---->\n          <div class=\"h-column h-column-container d-flex h-col-lg-auto h-col-md-auto h-col-auto style-1828-outer style-local-9546-c13-outer\">\n            <div data-colibri-id=\"9546-c13\" class=\"d-flex h-flex-basis h-column__inner h-px-lg-2 h-px-md-2 h-px-2 v-inner-lg-2 v-inner-md-2 v-inner-2 style-1828 style-local-9546-c13 position-relative\">\n              <!---->\n              <!---->\n              <div class=\"w-100 h-y-container h-column__content h-column__v-align flex-basis-100 align-self-lg-start align-self-md-start align-self-start\">\n                <!---->\n                <div data-colibri-id=\"9546-c14\" class=\"h-x-container style-1829 style-local-9546-c14 position-relative h-element\">\n                  <!---->\n                  <div class=\"h-x-container-inner style-dynamic-9546-c14-group\">\n                    <!----><span class=\"h-button__outer style-1830-outer style-local-9546-c15-outer d-inline-flex h-element\"><a  h-use-smooth-scroll=\"true\" href=\"https:\/\/www.maximebaczyk.fr\/\"  data-colibri-id=\"9546-c15\" class=\"d-flex w-100 align-items-center h-button justify-content-lg-center justify-content-md-center justify-content-center style-1830 style-local-9546-c15 position-relative\"><!----><!----> <span >Retour \u00e0 la page d&rsquo;accueil<\/span><\/a>\n                    <\/span>\n                  <\/div>\n                <\/div>\n              <\/div>\n            <\/div>\n          <\/div>\n        <\/div>\n      <\/div>\n    <\/div>\n  <\/div>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>Ces notes constituent une introduction au mod\u00e8le d&rsquo;Ising ainsi qu&rsquo;\u00e0 ses applications en physique statistique, surtout centr\u00e9es autour de la th\u00e9orie des transitions de phases et des ph\u00e9nom\u00e8nes critiques. Une transition de phases dans un syst\u00e8me macroscopique, c&rsquo;est \u00e0 dire constitu\u00e9 par un nombre gigantesque d&rsquo;atomes, correspond \u00e0 un changement radical de l&rsquo;\u00e9tat du syst\u00e8me [&hellip;]<\/p>\n","protected":false},"author":16,"featured_media":11375,"parent":231,"menu_order":2,"comment_status":"closed","ping_status":"closed","template":"page-templates\/full-width-page.php","meta":{"footnotes":""},"class_list":["post-9546","page","type-page","status-publish","has-post-thumbnail","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v21.5 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Ph\u00e9nom\u00e8nes critiques | Page Personnelle de Maxime Baczyk<\/title>\n<meta name=\"description\" content=\"Mes notes de cours de m\u00e9canique statistique sur la th\u00e9orie des transitions de phases et des ph\u00e9nom\u00e8nes critiques\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, 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