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arXiv:1210.1437 · Physical Review E

Critical line of honeycomb-lattice anisotropic Ising antiferromagnets in a field

S. L. A. de Queiroz

Published Feb 13, 2013• 2 citations
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Abstract

Numerical transfer-matrix methods are used to discuss the shape of the phase diagram, in field-temperature parameter space, of two-dimensional honeycomb-lattice Ising spin-1/2 magnets, with antiferromagnetic couplings along at least one lattice axis, in a uniform external field. Both the order and universality class of the underlying phase transition are examined as well. Our results indicate that in one particular case, the critical line has, at least to a very good approximation, a horizontal section (i.e., at constant field) of finite length, starting at the zero-temperature end of the phase boundary. Other than that, we find no evidence of unusual behavior, at variance with the re-entrant features predicted in earlier studies.

DOI
10.1103/physreve.87.024102

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Numerical transfer-matrix methods are used to discuss the shape of the phase diagram, in field-temperature parameter space, of two-dimensional honeycomb-lattice Ising spin-1/2 magnets, with antiferromagnetic couplings along at least one lattice axis, in a uniform external field. Both the order and universality class of the underlying phase transition are examined as well. Our results indicate that in one particular case, the critical line has, at least to a very good approximation, a horizontal section (i.e., at constant field) of finite length, starting at the zero-temperature end of the phase boundary. Other than that, we find no evidence of unusual behavior, at variance with the re-entrant features predicted in earlier studies.
Transfer-matrix methods are used, in conjunction with finite-size scaling and conformal invariance concepts, to generate an accurate phase diagram for a two-dimensional square-lattice Ising spin-1/2 magnet, with couplings which are positive along one coordinate axis and negative along the other, in a uniform external field. Our results indicate that the critical line starts horizontally at the zero-temperature end of the phase boundary, at variance with the re-entrant behavior predicted in some earlier studies. Estimates of the thermal scaling exponent are very close to the Ising value y(T)=1 along the critical line, except near T=0 , where strong crossover effects prevent a reliable analysis.
Abstract We study the critical properties of the antiferromagnetic spin-1/2 Ising model in an external field on the square lattice. Using tomographic entropic sampling, a flat-histogram simulation method, we estimate the number of configurations, , and related microcanonical averages in the energy-magnetization space, for system sizes L = 10–30. The critical line and exponents are calculated using finite-size scaling analysis in the temperature-external field plane. With these estimates in hand, we perform detailed studies of critical behavior using Metropolis sampling of larger systems ( ). These results are compared to several approximate theoretical methods. Our estimates of critical exponents and Binder’s reduced fourth cumulant along the critical line are in very good agreement with their respective literature values for the two-dimensional Ising universality class. We verify as well that the specific heat scales along the critical line, as expected for an Ising-like critical point.
Using large-scale quantum Monte Carlo simulations, we determine the ground state phase diagram of the spin-1/2 antiferromagnetic Heisenberg model on the honeycomb lattice for the most generic case of three varying interaction strengths along the different lattice directions. We identify continuous quantum phase transition lines that separate the long-range ordered antiferromagnetic regime from three distinct quantum-disordered phases, each characterized by dominant dimer-singlet formations. The finite-size behavior along these phase transition lines exhibits anomalously large corrections to scaling, which we relate to similar recent findings in certain dimerized quantum spin systems and to singular one-dimensional limits in the model parameter space. We also comment more generally on the nonuniversality of critical cumulant ratios in anisotropic systems and attempts to restore universality by varying the aspect ratio.
We have studied the antiferromagnetic Ising chain in a transverse magnetic field hx{h}_{x}hx​ and uniform longitudinal field hz.{h}_{z}.hz​. Using the density-matrix renormalization group calculation combined with a finite-size scaling the ground-state phase diagram in (hx,hz){(h}_{x}{,h}_{z})(hx​,hz​) plane is determined. It is shown that there is an order-disordered transition line in this plane and the critical properties belong to the universality class of the two-dimensional Ising model. Based on the perturbation theory in hz{h}_{z}hz​ the scaling behavior of the mass gap in the vicinity of the critical point (hx=1/2,hz=0){(h}_{x}{=1/2,h}_{z}=0)(hx​=1/2,hz​=0) is established. It is found that the form of the transition line near the classical multicritical point (hx=0,hz=1){(h}_{x}{=0,h}_{z}=1)(hx​=0,hz​=1) is linear. The connection of the considered quantum model with the quasi-one-dimensional classical Ising model in the magnetic field is discussed.
Transfer-matrix methods, with the help of finite-size scaling and conformal invariance concepts, are used to investigate the critical behavior of two-dimensional square-lattice Ising spin-1/2 systems with first- and second-neighbor interactions, both antiferromagnetic, in a uniform external field. On the critical curve separating collinearly ordered and paramagnetic phases, our estimates of the conformal anomaly c are very close to unity, indicating the presence of continuously varying exponents. This is confirmed by direct calculations, which also lend support to a weak-universality picture; however, small but consistent deviations from the Ising-like values η=1/4, γ/ν=7/4, β/ν=1/8 are found. For higher fields, on the line separating row-shifted (2×2) and disordered phases, we find values of the exponent η very close to zero.