���6����C�.C 766.7 715.6 766.7 0 0 715.6 613.3 562.2 587.8 881.7 894.4 306.7 332.2 511.1 511.1 531.3 531.3 413.2 413.2 295.1 531.3 531.3 649.3 531.3 295.1 885.4 795.8 885.4 443.6 542.4 542.4 456.8 513.9 1027.8 513.9 513.9 513.9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 << 963 963 1222.2 1222.2 963 963 1222.2 963] endobj Furthermore, the model may be applied to several modern … 846.3 938.8 854.5 1427.2 1005.7 973 878.4 1008.3 1061.4 762 711.3 774.4 785.2 1222.7 531.3 531.3 531.3 531.3 708.3 472.2 510.4 767.4 826.4 531.3 914.9 1033 826.4 253.5 Ground state in the thermodynamic limit. /FirstChar 33 /LastChar 196 /FirstChar 33 571 285.5 314 542.4 285.5 856.5 571 513.9 571 542.4 402 405.4 399.7 571 542.4 742.3 500 555.6 527.8 391.7 394.4 388.9 555.6 527.8 722.2 527.8 527.8 444.4 500 1000 500 511.1 511.1 511.1 831.3 460 536.7 715.6 715.6 511.1 882.8 985 766.7 255.6 511.1] /Name/F2 << /LastChar 196 << /Widths[285.5 513.9 856.5 513.9 856.5 799.4 285.5 399.7 399.7 513.9 799.4 285.5 342.6 460 511.1 306.7 306.7 460 255.6 817.8 562.2 511.1 511.1 460 421.7 408.9 332.2 536.7 endobj /Widths[350 602.8 958.3 575 958.3 894.4 319.4 447.2 447.2 575 894.4 319.4 383.3 319.4 /FontDescriptor 14 0 R 770.7 628.1 285.5 513.9 285.5 513.9 285.5 285.5 513.9 571 456.8 571 457.2 314 513.9 In the two-dimensional Heisenberg model the order is absent at T ≠ 0 (see, for instance, Patashinskii and Pokrovsky, 1979). 295.1 826.4 501.7 501.7 826.4 795.8 752.1 767.4 811.1 722.6 693.1 833.5 795.8 382.6 Rotational symmetry. 1222.2 1222.2 963 365.7 1222.2 833.3 833.3 1092.6 1092.6 0 0 703.7 703.7 833.3 638.9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 643.8 839.5 787 710.5 682.1 763 734.6 787 734.6 /FontDescriptor 41 0 R 44 0 obj 511.1 575 1150 575 575 575 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 /LastChar 196 460 664.4 463.9 485.6 408.9 511.1 1022.2 511.1 511.1 511.1 0 0 0 0 0 0 0 0 0 0 0 575 1041.7 1169.4 894.4 319.4 575] /FirstChar 33 >> >> 319.4 958.3 638.9 575 638.9 606.9 473.6 453.6 447.2 638.9 606.9 830.6 606.9 606.9 /FontDescriptor 17 0 R /FontDescriptor 20 0 R The Ising model can then be viewed as a limit of the Heisenberg model when the couplings in the x-y plane vanish. Heisenberg model. 295.1 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 295.1 295.1 531.3 826.4 826.4 826.4 826.4 0 0 826.4 826.4 826.4 1062.5 531.3 531.3 826.4 826.4 424.4 552.8 552.8 552.8 552.8 552.8 813.9 494.4 915.6 735.6 824.4 635.6 975 1091.7 30 0 obj endobj 799.2 642.3 942 770.7 799.4 699.4 799.4 756.5 571 742.3 770.7 770.7 1056.2 770.7 727.8 813.9 786.1 844.4 786.1 844.4 0 0 786.1 552.8 552.8 319.4 319.4 523.6 302.2 << 42 0 obj /LastChar 196 �t�DB�A,���xn!�U�e�T���f�sl`����ݙgTDΌx�nzś��٪�Ϯ��n!�am��aJ�HIV9U��ծ҄�SY���g�k-���JA�^�C��Skj�L�x&� /Subtype/Type1 /LastChar 196 /Name/F1 We'll leave the shape and dimensionality of the lattice unspecified for now. @���xwq"�{�/{*�H�����y*�7{Z0U����8M"����N@��v�j. /Widths[306.7 514.4 817.8 769.1 817.8 766.7 306.7 408.9 408.9 511.1 766.7 306.7 357.8 /FirstChar 33 571 285.5 314 542.4 285.5 856.5 571 513.9 571 542.4 402 405.4 399.7 571 542.4 742.3 /Name/F6 The Heisenberg-Ising spin ladder is one of the few short-range models showing con ne-ment of elementary excitations without the need of an external eld, neither transverse nor longitudinal. Unfortunately, there isn't much in nature that can be modeled very well by it. H ^ = − ∑ i j J S ^ i z S ^ j z. are widely applied in the field of condensed matter to understand magnetic systems. 750 708.3 722.2 763.9 680.6 652.8 784.7 750 361.1 513.9 777.8 625 916.7 750 777.8 /BaseFont/RZRXTL+CMSL9 15 0 obj 875 531.3 531.3 875 849.5 799.8 812.5 862.3 738.4 707.2 884.3 879.6 419 581 880.8 787 0 0 734.6 629.6 577.2 603.4 905.1 918.2 314.8 341.1 524.7 524.7 524.7 524.7 524.7 /Subtype/Type1 863.9 786.1 863.9 862.5 638.9 800 884.7 869.4 1188.9 869.4 869.4 702.8 319.4 602.8 /BaseFont/CXDXHS+CMR10 The Ising model (/ ˈ aɪ s ɪ ŋ /; German: ), named after the physicist Ernst Ising, is a mathematical model of ferromagnetism in statistical mechanics.The model consists of discrete variables that represent magnetic dipole moments of atomic "spins" that can be in one of two states (+1 or −1). 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 963 379.6 963 638.9 963 638.9 963 963 531.3] /BaseFont/EDELKZ+CMSY8 /LastChar 196 319.4 552.8 552.8 552.8 552.8 552.8 552.8 552.8 552.8 552.8 552.8 552.8 319.4 319.4 /FontDescriptor 38 0 R /Widths[295.1 531.3 885.4 531.3 885.4 826.4 295.1 413.2 413.2 531.3 826.4 295.1 354.2 Statistics of the lattice gas. >> 545.5 825.4 663.6 972.9 795.8 826.4 722.6 826.4 781.6 590.3 767.4 795.8 795.8 1091 0 0 0 0 0 0 691.7 958.3 894.4 805.6 766.7 900 830.6 894.4 830.6 894.4 0 0 830.6 670.8 /LastChar 196 Originally, it was invented for the phase transition of ferromagnets at the Curie temperature; however, in the course of time it was realized that with only slight changes the model can also be applied to other phase transitions, like order-disorder transitions in binary alloys. 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 627.2 817.8 766.7 692.2 664.4 743.3 715.6 /LastChar 196 /FontDescriptor 35 0 R /Name/F10 277.8 305.6 500 500 500 500 500 750 444.4 500 722.2 777.8 500 902.8 1013.9 777.8

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