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Physical review. B, Condensed matter

Nonuniversal Ising-like transition in two-dimensional XY spin systems induced by an external magnetic field

P. Azaria, H. T. Diep

Published Jan 1, 1989• 5 citations
Publisher

Abstract

Extensive Monte Carlo simulations have been performed to study the effect of an applied magnetic field in a two-dimensional system of $\mathrm{XY}$ spins interacting with each other via ferromagnetic and antiferromagnetic bonds. The magnetic field H reduces the system symmetry O(2) in spin space to ${Z}_{2}$. We show that there exists a critical value of H below which an Ising-like transition occurs. However, there remain continuous degrees of freedom so that critical exponents deviate from those of the pure Ising model.

DOI
10.1103/physrevb.39.745

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Extensive Monte Carlo simulations have been performed to study the effect of an applied magnetic field in a two-dimensional system of XY\mathrm{XY}XY spins interacting with each other via ferromagnetic and antiferromagnetic bonds. The magnetic field H reduces the system symmetry O(2) in spin space to Z2{Z}_{2}Z2​. We show that there exists a critical value of H below which an Ising-like transition occurs. However, there remain continuous degrees of freedom so that critical exponents deviate from those of the pure Ising model.
We study, by a Migdal-Kadanoff approximation and Monte Carlo simulations, the phase diagram of a two-dimensional coupled XY-Ising model. This model can describe phase transitions in different systems with underlying continuous and Z2{\mathit{Z}}_{2}Z2​ symmetries. Depending on the parameters, we find separate XY, Ising and first-order transitions. Also, a line of continuous transitions is found with simultaneous loss of XY and Ising order and varying critical exponents. The fully frustrated XY and Josephson-junction systems can be considered to lie along different paths in the model which can result in nonuniversal behavior if the transition is a single one.
In the framework of mean field approximation, we consider a spin system consisting of two interacting sub-ensembles. The intra-ensemble interactions are ferromagnetic, while the inter-ensemble interactions are antiferromagnetic. We define the effective number of the nearest neighbors and show that if the two sub-ensembles have the same effective number of the nearest neighbors, the classical form of critical exponents (α=0, β=1/2, γ=γ'=1, δ=3) gives way to the non-classical form (α=0, β=3/2, γ=γ'=0, δ=1), and the scaling function changes simultaneously. We demonstrate that this system allows for two second-order phase transitions and two first-order phase transitions. We observe that an external magnetic field does not destroy the phase transitions but only shifts their critical points, allowing for control of the system's parameters. We discuss the regime when the magnetization as a function of the magnetic field develops a low-magnetization plateau and show that the height of this plateau abruptly rises to the value of one when the magnetic field reaches a critical value. Our analytical results are supported by a Monte Carlo simulation of a three-dimensional layered model.
We study the critical properties of the two-dimensional (2D) XY\mathrm{XY}XY model in a transverse magnetic field with filling factors f=1/3f=1/3f=1/3 and 2/5.2/5.2/5. To obtain a comparison with recent experiments, we investigate the effect of weak quenched bond disorder for f=2/5.f=2/5.f=2/5. A finite-size scaling analysis of extensive Monte Carlo simulations strongly suggests that the critical exponents of the phase transition for f=1/3f=1/3f=1/3 and for f=2/5f=2/5f=2/5 with disorder are those of the pure 2D Ising model. The relevant low-energy excitations are domain walls, and we show that their properties determine the nature of the phase transition.
We compare the critical properties of the two-dimensional (2D) XY\mathrm{XY}XY model in a transverse magnetic field with filling factors f=1/3f\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/3f=1/3 and 2/52/52/5. To obtain a comparison with recent experiments, we investigate the effect of weak quenched bond disorder for f=2/5f\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2/5f=2/5. A finite-size scaling analysis of extensive Monte Carlo simulations strongly suggests that the critical exponents of the phase transition for f=1/3f\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1/3f=1/3, and for f=2/5f\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2/5f=2/5 with disorder, are those of the pure 2D Ising model. Studying the possible domain walls in the system provides some explanations for our results.
Using the Monte Carlo Simulation (MCS) method combined with the Metropolis algorithm, we explore the magnetic properties of a two-dimensional (2D) spin system with spins 1, 2 and 3. The adapted simulation to the Ising model aims to study the impact of the correction term a of the interaction with second neighbors and the crystal field D on the critical temperature [Formula: see text] of the 2D anisotropic square lattice for different integer values of spins. The obtained results demonstrate that the critical temperature [Formula: see text] is significantly affected by the competing interactions between the anisotropy parameter, second-neighbor interaction and the crystal field. The considered model exhibits a critical phase transition regardless of the spin S value where the critical temperature increases with the value of S. Note that this phase transition occurs under the condition [Formula: see text]. Moreover, the obtained results show that the complex interactions give rise to a variety of phase diagrams, thereby revealing the richness of possible magnetic behaviors in the studied system.
We use Monte Carlo and transfer matrix methods in combination with extrapolation schemes to determine the phase diagram of the two-dimensional superantiferromagnetic (SAF) Ising model with next-nearest-neighbor (NNN) interactions in a magnetic field. The interactions between nearest-neighbor (NN) spins are ferromagnetic along x, and antiferromagnetic along Y. We find that for sufficiently low temperatures and fields, there exists a region limited by a critical line of second-order transitions separating a SAF phase from a magnetically induced paramagnetic phase. We did not find any region with either first-order transition or with reentrant behavior. The NNN couplings produce either an expansion or a contraction of the SAF phase. Expansion occurs when the interactions are antiferromagnetic, and contraction when they are ferromagnetic. There is a critical ratio R(c)=1/2 between NNN and NN couplings, beyond which the SAF phase no longer exists.