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Recently we showed that the critical nonequilibrium relaxation in the Swendsen-Wang algorithm is widely described by the stretched-exponential relaxation of physical quantities in the Ising or Heisenberg models. Here we make a similar analysis in the Berezinsky-Kosterlitz-Thouless phase transition in the two-dimensional (2D) XY model and in the first-order phase transition in the 2D q = 5 Potts model and find that these phase transitions are described by the simple exponential relaxation and power-law relaxation of physical quantities, respectively. We compare the relaxation behaviors of these phase transitions with those of the second-order phase transition in the three- and four-dimensional XY models and in the 2D q-state Potts models for 2 ≤ q ≤ 4 and show that the species of phase transitions can be clearly characterized by the present analysis. We also compare the size dependence of relaxation behaviors of the first-order phase transition in the 2D q = 5 and 6 Potts models and propose a quantitative criterion on "weakness" of the first-order phase transition. [ABSTRACT FROM AUTHOR]

Motivated by puzzling aspects of spin-glass behavior reported in frustrated magnetic materials, we theoretically investigate effects of magnetoelastic coupling in geometrically frustrated classical spin models. In particular, we consider bond-disordered Heisenberg antiferromagnets on a pyrochlore lattice coupled to local lattice distortions. By integrating out the lattice degree of freedom, we derive an effective spin-only model, the bilinear-biquadratic model with bond disorder. The effective model is analyzed by classical Monte Carlo simulations using an extended loop algorithm. First, we discuss the phase diagrams in detail by showing the comprehensive Monte Carlo data for thermodynamic and magnetic properties. We show that the spin-glass transition temperature Tf is largely enhanced by the spin-lattice coupling b in the weakly disordered regime. By considering the limit of strong spin-lattice coupling, this enhancement is ascribed to the suppression of thermal fluctuations in semidiscrete degenerate manifold formed in the presence of the spin-lattice coupling. We also find that, by increasing the strength of disorder Δ, the system shows a concomitant transition of the nematic order and spin glass at a temperature determined by b, being almost independent of Δ. This is due to the fact that the spin-glass transition is triggered by the spin collinearity developed by the nematic order. Although further-neighbor exchange interactions originating in the cooperative lattice distortions result in spin-lattice order in the weakly disordered regime, the concomitant transition remains robust with Tf almost independent of Δ. We find that the magnetic susceptibility shows hysteresis between the field-cooled and zero-field-cooled data below Tf, and that the nonlinear susceptibility shows a negative divergence at the transition. These features are common to conventional spin-glass systems. Meanwhile, we find that the specific heat exhibits a broad peak at Tf, and that the Curie-Weiss temperature varies with Δ, even in the region where Tf is insensitive to Δ. In addition, we clarified that the concomitant transition remains robust against a substantial external magnetic field. These features are in clear contrast to the conventional spin-glass behavior. Furthermore, we show that the cubic susceptibility obeys a Curie-Weiss'type law and the estimated "Curie-Weiss" temperature gives a good measure of the spin-lattice coupling even in the presence of bond randomness. We also show, by studying single-spin-flip dynamics in the nematic phase, that the glassy spin dynamics may be observed at a rather high temperature in a realistic situation for weak disorder. All these results are discussed in comparison with experiments for typical pyrochlore magnets, such as Y2Mo2O7 and ZnCr2O4. [ABSTRACT FROM AUTHOR]

At low temperatures, the two-dimensional continuous-spin systems exhibit large correlation lengths. Some of them show the Berezinskii-Kosterlitz-Thouless-like transitions, and some others show pseudocritical behaviors for which correlation lengths are extremely large but finite. To distinguish pseudo and genuine critical behaviors, it is important to understand the nature of spin-spin correlations and topological defects at low temperatures in continuous-spin systems. In this paper, I develop a finite-size scaling analysis which is suitable for distinguishing the critical behavior and its applications to the two-dimensional XY, Heisenberg, and RP² models. [ABSTRACT FROM AUTHOR]

Although the nonequilibrium-relaxation (NER) method has been widely used in Monte Carlo studies on phase transitions in classical spin systems, such studies have been quite limited in quantum phase transitions. The reason is that the relaxation process based on cluster-update quantum Monte Carlo (QMC) algorithms, which are now standards in Monte Carlo studies on quantum systems, has been considered "too fast" for such analyses. Recently, the present authors revealed that the NER process in classical spin systems based on cluster-update algorithms is characterized by stretched-exponential critical relaxation, rather than conventional power-law relaxation in local-update algorithms. In the present article, we show that this is also the case in quantum phase transitions analyzed with the cluster-update QMC. As the simplest example of isotropic quantum spin models that exhibit quantum phase transitions, we investigate the Néel-dimer quantum phase transition in the two-dimensional S = 1 / 2 columnar-dimerized antiferromagnetic Heisenberg model with the continuous-time loop algorithm, and we confirm stretched-exponential critical relaxation consistent with the three-dimensional classical Heisenberg model in the Swendsen-Wang algorithm. [ABSTRACT FROM AUTHOR]

We investigate nonequilibrium relaxations of Ising models at the critical point by using a cluster update. While preceding studies imply that nonequilibrium cluster-flip dynamics at the critical point are universally described by the stretched-exponential function, we find that the dynamics changes from the stretched exponential to the power function as the dimensionality is increased: The two-, three-, four-, and infinite-dimensional Ising models are numerically studied, and the four- and infinite-dimensional Ising models exhibit the power-law relaxation. We also show that the finite-size scaling analysis using the normalized correlation length is markedly effective for the analysis of relaxational processes rather than the direct use of the Monte Carlo step. [ABSTRACT FROM AUTHOR]

A method is introduced to measure the entanglement entropy using a wavelet analysis. Using this method, the two-dimensional Haar wavelet transform of a configuration of Fortuin-Kasteleyn (FK) clusters is performed. The configuration represents a direct snapshot of spin-spin correlations since spin degrees of freedom are traced out in FK representation. A snapshot of FK clusters loses image information at each coarse-graining process by the wavelet transform. It is shown that the loss of image information measures the entanglement entropy in the Potts model. [ABSTRACT FROM AUTHOR]

We study critical and magnetic properties of a bilayer Ising system consisting of two triangular planes A and B, with the antiferromagnetic (AF) coupling JA and the ferromagnetic (FM) one JB for the respective layers, which are coupled by the interlayer interaction JAB by using Monte Carlo simulations. When JA and JB are of the same order, the unfrustrated FM plane orders first at a high temperature Tc1~JB. The spontaneous FM order then exerts influence on the other frustrated AF plane as an effective magnetic field, which subsequently induces a ferrimagnetic order in this plane at low temperatures below Tc2. When short-range order is developed in the AF plane while the influence of the FM plane is still small, there appears a preemptive Berezinskii-Kosterlitz-Thouless-type pseudocritical crossover regime just above the ferrimagnetic phase transition point, where the short-distance behavior up to a rather large length scale exponentially diverging in ∝JA/T is controlled by a line of Gaussian fixed points at T=0. In the crossover region, a continuous variation in the effective critical exponent 49≲ηeff≲1/2 is observed. The phase diagram by changing the ratio JA/JB is also investigated. [ABSTRACT FROM AUTHOR]

Relaxational processes in ordered phases of one-dimensional Ising models with long-range interactions are investigated by Monte Carlo simulations. Three types of spin model, the pure ferromagnetic, the diluted ferromagnetic, and the spin glass models, are examined. The effective dimension of the one-dimensional systems are controlled by a parameter σ, which tunes the rate of interaction decay. Systematical investigations of droplet dynamics, from the lower to the upper critical dimension, are conducted by changing the value of σ. Comparing numerical data with the droplet theory, it is found that the surface dimension of droplets is distributed around the effective dimension. The distribution in the surface dimension makes the droplet dynamics complex and extremely enhances dynamical crossover. [ABSTRACT FROM AUTHOR]

Recently, it was shown [Y. Nonomura, J. Phys. Soc. Jpn. 83, 113001 (2014)] that the nonequilibrium critical relaxation of the two-dimensional (2D) Ising model from a perfectly ordered state in the Wolff algorithm is described by stretched-exponential decay, and a universal scaling scheme was found to connect nonequilibrium and equilibrium behaviors. In the present study we extend these findings to vector spin models, and the 3D Heisenberg model could be a typical example. To evaluate the critical temperature and critical exponents precisely using the above scaling scheme, we calculate nonequilibrium ordering from the perfectly disordered state in the Swendsen-Wang algorithm, and we find that the critical ordering process is described by stretched-exponential growth with a comparable exponent to that of the 3D XY model. The critical exponents evaluated in the present study are consistent with those in previous studies. [ABSTRACT FROM AUTHOR]

We study response to a twist in the two-dimensional p-state clock model, which has the discrete Zp symmetry. The response is measured in terms of helicity modulus, which is usually defined with respect to an infinitesimal twist. However, we demonstrate that such a definition is inappropriate for the clock model. The helicity modulus must be defined with respect to a finite, quantized twist which matches the discrete Zp symmetry of the model. Numerical study of the appropriately defined helicity modulus resolves controversy over the clock model, showing the existence of two Berezinskii-Kosterlitz-Thouless transitions for p > 4 [ABSTRACT FROM AUTHOR]