Antiferromagnetic Ordering in an Ising Lattice by a Monte Carlo Method

J. Roberto Viana, Minos A. Neto, J. Ricardo de Sousa

Yasushi Honda, Adam Lipowski, Tsuyoshi Horiguchi

Seizo Watarai, Seiji Miyashita

Critical properties of the two successive phase transitions of Ising-like Heisenberg antiferromagnets on the hexagonal lattice are examined by the Monte Carlo method. In order to obtain the critical exponents, the finite size scaling methods are used for the lattice sizes of L =18 ∼ 48. Using the reweighting Monte Carlo method, the exponents at the higher critical temperature are estimated as 1/ν=1.481±0.019 and γ/ν=1.980±0.016, which agree with those of the 3DXY model. At the lower critical temperature, standard procedure of the reweighting method does not give values of the exponents with satisfactory precision. Thus we estimate the exponents carefully with aid of the ordinary Monte Carlo method at various temperatures near T c . The values of 1/ν≃ 1.48±0.006 and γ/ν≃1.97±0.050 are obtained and we conclude that those are consistent with the universality class of the 3DXY model.

Dennis C. Rapaport

M F Sykes, Michael Ellis Fisher

Jan Gukelberger, Lei Wang, Lode Pollet

We study the phase diagram of the two-dimensional repulsive Hubbard model with spin-dependent anisotropic hopping at half filling. The system develops Ising antiferromagnetic long-range order already at infinitesimal repulsive interaction strength in the ground state. Outside the perturbative regime, unbiased predictions for the critical temperatures of the Ising antiferromagnet are made for representative interaction values by a variety of state-of-the-art quantum Monte Carlo methods, including the diagrammatic Monte Carlo, continuous-time determinantal Monte Carlo, and path-integral Monte Carlo methods. Our findings are relevant to ultracold atom experiments in the $p$ orbital or with spin-dependent optical lattices.