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Journal of Physics Conference Series

A New Universality at a First-Order Phase Transition: The Spin-flop Transition in an Anisotropic Heisenberg Antiferromagnet

Jiahao Xu, Shan-Ho Tsai, David Paul Landau, Kurt Binder

Published Feb 1, 2020• 0 citations
Publisher

Abstract

Abstract A great triumph of statistical physics in the latter part of the 20th century was the understanding of critical behavior and universality at second-order phase transitions. In contrast, first-order transitions were believed to have no common features. However, we argue that the classic, first-order “spin-flop” transition (between the antiferromagnetic and the rotationally degenerate, canted state) in an anisotropic antiferromagnet in a magnetic field exhibits a new kind of universality. We present a finite-size scaling theory for a first-order phase transition where a continuous symmetry is broken using an approximation of Gaussian probability distributions with a phenomenological degeneracy factor “q” included, where “q” characterizes the relative degeneracy of the ordered phases. Predictions are compared with high resolution Monte Carlo simulations of the three-dimensional, XXZ Heisenberg antiferromagnet in a field to study the finite-size behavior for L×L×L simple cubic lattices. The field dependence of all moments of the order parameters exhibit universal intersections at the spin-flop transition. Our Monte Carlo data agree with theoretical predictions for asymptotic large L behavior. Our theory yields q = π, and we present numerical evidence that is compatible with this prediction. The agreement between the theory and simulation implies a heretofore unknown universality.

DOI
10.1088/1742-6596/1483/1/012004

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Abstract A great triumph of statistical physics in the latter part of the 20th century was the understanding of critical behavior and universality at second-order phase transitions. In contrast, first-order transitions were believed to have no common features. However, we argue that the classic, first-order “spin-flop” transition (between the antiferromagnetic and the rotationally degenerate, canted state) in an anisotropic antiferromagnet in a magnetic field exhibits a new kind of universality. We present a finite-size scaling theory for a first-order phase transition where a continuous symmetry is broken using an approximation of Gaussian probability distributions with a phenomenological degeneracy factor “q” included, where “q” characterizes the relative degeneracy of the ordered phases. Predictions are compared with high resolution Monte Carlo simulations of the three-dimensional, XXZ Heisenberg antiferromagnet in a field to study the finite-size behavior for L×L×L simple cubic lattices. The field dependence of all moments of the order parameters exhibit universal intersections at the spin-flop transition. Our Monte Carlo data agree with theoretical predictions for asymptotic large L behavior. Our theory yields q = π, and we present numerical evidence that is compatible with this prediction. The agreement between the theory and simulation implies a heretofore unknown universality.
Finite-size scaling for a first-order phase transition where a continuous symmetry is broken is developed using an approximation of Gaussian probability distributions with a phenomenological "degeneracy" factor included. Predictions are compared with data from Monte Carlo simulations of the three-dimensional, XXZ Heisenberg antiferromagnet in a field in order to study the finite-size behavior on a L×L×L simple cubic lattice for the first-order "spin-flop" transition between the Ising-like antiferromagnetic state and the canted, XY-like state. Our theory predicts that for large linear dimension L the field dependence of all moments of the order parameters as well as the fourth-order cumulants exhibit universal intersections. Corrections to leading order should scale as the inverse volume. The values of these intersections at the spin-flop transition point can be expressed in terms of a factor q that characterizes the relative degeneracy of the ordered phases. Our theory yields q=π, and we present numerical evidence that is compatible with this prediction. The agreement between the theory and simulation implies a heretofore unknown universality can be invoked for first-order phase transitions.
The disordering transition of half a monolayer of chemisorbed oxygen on Ru(001) can be classified in the universality class of the two-dimensional Heisenberg model with face-centered anisotropy. Theoretical studies of this class suggest fluctuation-induced first-order-transition behavior. Experimental study of the O/Ru(001) system, on the other hand, reveals a continuous phase transition with exponents near those of the three-state Potts model. We have investigated this discrepancy via Monte Carlo simulations of the Heisenberg model using the histogram method to determine transition order, focusing on two possible resolutions of the discrepancy: (1) finite-size rounding might be expected to render the experimental transition apparently continuous even if it is actually first order; or (2) transition order might depend on the details of the interaction energies. Despite its seeming inconsistency with the standard understanding of universality, we have strong evidence for the latter explanation; there appears to be a parameter regime of second-order behavior within standard ferromagnetic Heisenberg symmetry. We delineate this breakdown of universality and speculate as to its mechanism.
Finite size scaling for a first order phase transition, where a continuous symmetry is broken, is tested using an approximation of Gaussian probability distributions with a phenomenological "degeneracy" factor. Predictions are compared to the data from Monte Carlo simulations of the Lebwohl-Lasher model on L × L × L simple cubic lattices. The data show that the intersection of the fourth-order cumulant of the order parameter for different lattice sizes can be expressed in terms of the relative degeneracy q = 4π of the ordered and disordered phases. This result further supports the concept of universality at first order transitions developed recently.
Abstract In this work we use numerical Monte Carlo techniques to study the phase diagram of the three‐dimensional classical Heisenberg anti‐ferromagnetic (AF) model with single‐ion anisotropy model with an uniform magnetic field applied along the easy axis. Early experimental as well as theoretical calculations have shown that the phase diagram of the model is quite rich. We simulated the model on a simple cubic lattices using the Wang–Landau sampling and Metropolis algorithm. Finite size scaling theory is used to obtain the phase diagram. At low field and low temperature the system exhibits AF order separated from a spin‐flop (SF) phase by a first‐order line. As temperature grows a paramagnetic phase is reached by crossing a second‐order line both from the AF phase and from the SF phase. The critical exponents are obtained for each transition line. Contrary to early works we find that the line separating the SF phase from the paramagnetic phase is in the Ising class of universality.
The magnetization process of the one-dimensional antiferromagnetic Heisenberg model with the Ising-like anisotropic exchange interaction is studied by the exact diagonalization technique. It results in the evidence of the first-order spin-flop transition with a finite magnetization jump in the N\'eel ordered phase for S> 1.S>~1.S> 1. It implies that the S=12S=\frac{1}{2}S=21​ chain is an exceptional case where the metamagnetic transition becomes second order due to large quantum fluctuations.
The nature of the phase transition of antiferromagnetic vector spin models on the stacked triangular lattice (STA) has been an issue of debate. In order to account for the coplanar non-collinear order in the ground state one needs two vector fields in a Ginzburg–Landau–Wilson Hamiltonian. The field theoretical renormalization group analysis shows that there is a threshold value Nc for the number of spin component N, and for N > Nc the transition is of second order belonging to a new ‘‘chiral’’ universality class, while for N < Nc the chiral fixed points ceases to exist in the real parameter space and the transition is of first order. According to a recent estimate based on a Monte Carlo renormalization group study, 3 < Nc < 8. 2) Therefore a first order transition is expected for the physically relevant XY and Heisenberg spin systems. The phase transition of the XY or Heisenberg STA is of very weak first order and is said to be of ‘‘almost second order’’ with large (but finite) correlation lengths due to a slow velocity region in the renormalization group flow. Monte Carlo simulations on systems with moderate size appear to show second order transitions with pseudo-critical behavior. Strong first order transitions were found for variants of the model on which a constraint of local rigidity was imposed which still belong to the same universality class as the original STA. Recently the first order nature of the phase transition in XY antiferromagnet on the stacked triangular lattice (XY-STA model) was demonstrated directly by canonical Monte Carlo simulations on large systems, in which the energy probability distribution shows a double peak structure near the transition temperature. The purpose of the present paper is to show the first order transition of the XY-STA model by applying a novel technique: a microcanonical method. To distinguish a weak first order transition from a second order one can be difficult, especially if the energy jump, the characteristic of a first order transition, is tiny as is the case for frustrated spin systems. Limited to accessible system sizes one may analyze the different power law behavior of the maximum of specific heat or susceptibility, with an exponent equal to three for a first order transition and less than three for a second order transition. The obvious solution to increase the size of the system runs into difficulties for the canonical simulations (at constant temperature) because of the growing autocorrelation times. Also the histogram method is then restricted to smaller intervals of temperature shrinking as the inverse power of the system size. In this short note we will show that the microcanonical simulations (at constant energy) can help to solve the problems encountered in canonical simulations. The method has been tested for strong first order transitions and also for second order ones. Before presenting the method and the results we have to describe the model we study. It is given by the usual Hamiltonian