/BaseFont/FYCBAB+CMBX12 QAF can be characterized by a perfect AF order on the Ising as well as Heisenberg sublattice, while a perfect AF order between the nn Ising and Heisenberg spins is gradually destroyed when increasing ¢ from zero. /FirstChar 33 /BaseFont/RZRXTL+CMSL9 endobj << 535.6 641.1 613.3 302.2 424.4 635.6 513.3 746.7 613.3 635.6 557.8 635.6 602.2 457.8 687.5 312.5 581 312.5 562.5 312.5 312.5 546.9 625 500 625 513.3 343.8 562.5 625 312.5 787 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 Nevertheless, at this point one has to already stress that the Ising model represents a certain group of Ising-Heisenberg model Thread starter LagrangeEuler; Start date Jul 17, 2013; Jul 17, 2013 Translational symmetry. << I have found when temperature limits to zero specific heat of Ising model results as 0. 295.1 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 531.3 295.1 295.1 324.7 531.3 590.3 295.1 324.7 560.8 295.1 885.4 590.3 531.3 590.3 560.8 414.1 419.1 /Name/F5 680.6 777.8 736.1 555.6 722.2 750 750 1027.8 750 750 611.1 277.8 500 277.8 500 277.8 /Widths[319.4 552.8 902.8 552.8 902.8 844.4 319.4 436.1 436.1 552.8 844.4 319.4 377.8 511.1 575 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 0 513.9 770.7 456.8 513.9 742.3 799.4 513.9 927.8 1042 799.4 285.5 513.9] /BaseFont/DGNJWF+CMTI9 756.4 705.8 763.6 708.3 708.3 708.3 708.3 708.3 649.3 649.3 472.2 472.2 472.2 472.2 /LastChar 196 /FontDescriptor 29 0 R Bethe's ansatz . 39 0 obj Assuming the AF Heisenberg coupling (J > 0), one always flnds the quantum anti-ferromagnetic phase (QAF) to occur in the ground state. 795.8 795.8 649.3 295.1 531.3 295.1 531.3 295.1 295.1 531.3 590.3 472.2 590.3 472.2 336.8 826.4 501.7 501.7 708.3 708.3 708.3 678.8 767.4 637.2 607.6 708.3 750 295.1 /Type/Font 566.7 843 683.3 988.9 813.9 844.4 741.7 844.4 800 611.1 786.1 813.9 813.9 1105.5 /Type/Font /BaseFont/ITPEES+CMCSC10 /Widths[285.5 513.9 856.5 513.9 856.5 799.4 285.5 399.7 399.7 513.9 799.4 285.5 342.6 591.1 613.3 613.3 835.6 613.3 613.3 502.2 552.8 1105.5 552.8 552.8 552.8 0 0 0 0 799.2 642.3 942 770.7 799.4 699.4 799.4 756.5 571 742.3 770.7 770.7 1056.2 770.7 295.1 826.4 501.7 501.7 826.4 795.8 752.1 767.4 811.1 722.6 693.1 833.5 795.8 382.6 531.3 531.3 531.3 531.3 708.3 472.2 510.4 767.4 826.4 531.3 914.9 1033 826.4 253.5 15 0 obj One is due to Lenz (1920), and was later on worked out in detail by his pupil Ising (1925). 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 642.3 856.5 799.4 713.6 685.2 770.7 742.3 799.4 413.2 590.3 560.8 767.4 560.8 560.8 472.2 531.3 1062.5 531.3 531.3 531.3 0 0 0 0 Partition Function Critical Temperature Ising Model Heisenberg Model Spontaneous Magnetization These keywords were added by machine and not by the authors. /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 /Name/F7 285.5 513.9 513.9 513.9 513.9 513.9 513.9 513.9 513.9 513.9 513.9 513.9 285.5 285.5 << endobj 863.9 786.1 863.9 862.5 638.9 800 884.7 869.4 1188.9 869.4 869.4 702.8 319.4 602.8 898.1 898.1 963 963 768.5 989.9 813.3 678.4 961.2 671.3 879.9 746.7 1059.3 709.3 306.7 766.7 511.1 511.1 766.7 743.3 703.9 715.6 755 678.3 652.8 773.6 743.3 385.6 319.4 575 319.4 319.4 559 638.9 511.1 638.9 527.1 351.4 575 638.9 319.4 351.4 606.9 endobj /FontDescriptor 14 0 R 963 963 0 0 963 963 963 1222.2 638.9 638.9 963 963 963 963 963 963 963 963 963 963 Rotational symmetry. 513.9 829.3 456.8 513.9 742.3 799.4 513.9 927.8 1042 799.4 285.5 513.9] endobj 44 0 obj 883.7 823.9 884 833.3 833.3 833.3 833.3 833.3 768.5 768.5 574.1 574.1 574.1 574.1 813.9 813.9 669.4 319.4 552.8 319.4 552.8 319.4 319.4 613.3 580 591.1 624.4 557.8 875 531.3 531.3 875 849.5 799.8 812.5 862.3 738.4 707.2 884.3 879.6 419 581 880.8 /FontDescriptor 20 0 R /LastChar 196 /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 /Type/Font /Name/F10 638.9 638.9 509.3 509.3 379.6 638.9 638.9 768.5 638.9 379.6 1000 924.1 1027.8 541.7 If we let the coupling in the z-direction vanish, then we have the XY … 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] 708.3 795.8 767.4 826.4 767.4 826.4 0 0 767.4 619.8 590.3 590.3 885.4 885.4 295.1 /Type/Font xڍY�s�:��_����D}��l����t&���K҃"�6����R��_���d;�{���$ � &�Dۀ~~�q���e�o�,2�Y,�,������[��< �CW�M�x6��;��ߪ�O�m�WYVO-�U�řn���6Nw�$ /Name/F1 This process is experimental and the keywords may be updated as the learning algorithm improves. And I meant Quantum Heisenberg model which Hamiltanian is invarian only under spins swaping. 531.3 531.3 413.2 413.2 295.1 531.3 531.3 649.3 531.3 295.1 885.4 795.8 885.4 443.6 846.3 938.8 854.5 1427.2 1005.7 973 878.4 1008.3 1061.4 762 711.3 774.4 785.2 1222.7 277.8 500 555.6 444.4 555.6 444.4 305.6 500 555.6 277.8 305.6 527.8 277.8 833.3 555.6 /FirstChar 33 H ^ = − ∑ i j J S ^ i z S ^ j z. are widely applied in the field of condensed matter to understand magnetic systems. The wavefunction. /FontDescriptor 11 0 R Twisted lattice gas. /BaseFont/NVGHTU+CMR9 850.9 472.2 550.9 734.6 734.6 524.7 906.2 1011.1 787 262.3 524.7] /FontDescriptor 38 0 R And I'm considering some, that I belive one could call 3D Ising model (see link to the article in post). /FirstChar 33 /Subtype/Type1 527.8 314.8 524.7 314.8 314.8 524.7 472.2 472.2 524.7 472.2 314.8 472.2 524.7 314.8 542.4 542.4 456.8 513.9 1027.8 513.9 513.9 513.9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 675.9 937.5 875 787 750 879.6 812.5 875 812.5 875 0 0 812.5 >> /Filter[/FlateDecode] /Name/F12 >> The Ising model can then be viewed as a limit of the Heisenberg model when the couplings in the x-y plane vanish. 277.8 500] /Name/F11 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 Statistics of the lattice gas. /Type/Font /LastChar 196 The model and its symmetries . /Type/Font /FirstChar 33 /BaseFont/EDELKZ+CMSY8 /LastChar 196 656.3 625 625 937.5 937.5 312.5 343.8 562.5 562.5 562.5 562.5 562.5 849.5 500 574.1 (���q�;0ᆎ-t4#��Z�w1�P�p:>�2� ��8��j�\�I{>B ��������K��jӀ�,"}��O�T���2�O4�}X�ӈ/I /FontDescriptor 41 0 R one gets to the idea of the Ising model. 343.8 593.8 312.5 937.5 625 562.5 625 593.8 459.5 443.8 437.5 625 593.8 812.5 593.8 What we are going to find – a preview. /LastChar 196 /Type/Font /FontDescriptor 8 0 R 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 643.8 839.5 787 710.5 682.1 763 734.6 787 734.6 473.8 498.5 419.8 524.7 1049.4 524.7 524.7 524.7 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 The time-dependent autocorrelation and correlation functions are calculated for the spin-1/2 Ising-Heisenberg doubly decorated planar model in order to elucidate the mutual in°uence of quantum and thermal °uctuations on the spin dynamics. Well-separated particles. ��9UlY�B$��r�=�'�u �� ID�0����hp���3Ǡ�U������9���h��A�%�y*�!���삁Ǘk�C�����1#���F�}���Z�du����UN�cؾ��-�Jň�z1G�� /FontDescriptor 35 0 R 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 endobj In the two-dimensional Heisenberg model the order is absent at T ≠ 0 (see, for instance, Patashinskii and Pokrovsky, 1979). /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 /LastChar 196 And in its simplified version, the Ising model. 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 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 /FontDescriptor 17 0 R 36 0 obj Heisenberg model. 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 642.3 856.5 799.4 713.6 685.2 770.7 742.3 799.4 endobj /Widths[1062.5 531.3 531.3 1062.5 1062.5 1062.5 826.4 1062.5 1062.5 649.3 649.3 1062.5 30 0 obj 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 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 0 578.1 885.4 826.4 649.3 708.3 /Type/Font /FirstChar 33 708.3 708.3 826.4 826.4 472.2 472.2 472.2 649.3 826.4 826.4 826.4 826.4 0 0 0 0 0 770.7 628.1 285.5 513.9 285.5 513.9 285.5 285.5 513.9 571 456.8 571 457.2 314 513.9 >> 285.5 513.9 513.9 513.9 513.9 513.9 513.9 513.9 513.9 513.9 513.9 513.9 285.5 285.5 750 708.3 722.2 763.9 680.6 652.8 784.7 750 361.1 513.9 777.8 625 916.7 750 777.8