Global persistence exponent of the double-exchange model

We obtained the global persistence exponent $\theta_g$ for a continuous spin model on the simple cubic lattice with double-exchange interaction by using two different methods. First, we estimated the exponent $\theta_g$ by following the time evolution of probability $P(t)$ that the order parameter of the model does not change its sign up to time $t$ $[P(t)\thicksim t^{-\theta_g}]$. Afterwards, that exponent was estimated through the scaling collapse of the universal function $L^{\theta_g z} P(t)$ for different lattice sizes. Our results for both approaches are in very good agreement each other.Comment: 4 pages, 3 figures, and 3 tables. To appear in Physical Review

Short-time critical dynamics of the Baxter-Wu model

We study the early time behavior of the Baxter-Wu model, an Ising model with three-spin interactions on a triangular lattice. Our estimates for the dynamic exponent $z$ are compatible with results recently obtained for two models which belong to the same universality class of the Baxter-Wu model: the two-dimensional four-state Potts model and the Ising model with three-spin interactions in one direction. However, our estimates for the dynamic exponent $\theta$ of the Baxter-Wu model are completely different from the values obtained for those models. This discrepancy could be related to the absence of a marginal operator in the Baxter-Wu model.Comment: 7 pages, 11 figures, accepted for publication in Phys. Rev.

A connection between the Ice-type model of Linus Pauling and the three-color problem

The ice-type model proposed by Linus Pauling to explain its entropy at low temperatures is here approached in a didactic way. We first present a theoretically estimated low-temperature entropy and compare it with numerical results. Then, we consider the mapping between this model and the three-colour problem, i.e.,colouring a regular graph with coordination equal to 4 (a two-dimensional lattice) with three colours, for which we apply the transfer-matrix method to calculate all allowed configurations for two-dimensional square lattices of $N$ oxygen atoms ranging from 4 to 225. Finally, from a linear regression of the transfer matrix results, we obtain an estimate for the case $N\rightarrow \infty$ which is compared with the exact solution by Lieb.Comment: 25 pages, 10 figure

Short-time behavior of a classical ferromagnet with double-exchange interaction

We investigate the critical dynamics of a classical ferromagnet on the simple cubic lattice with double-exchange interaction. Estimates for the dynamic critical exponents $z$ and $\theta$ are obtained using short-time Monte Carlo simulations. We also estimate the static critical exponents $\nu$ and $\beta$ studying the behavior of the samples at an early time. Our results are in good agreement with available estimates and support the assertion that this model and the classical Heisenberg model belong to the same universality class

Dynamic critical exponents of the Ising model with multispin interactions

We revisit the short-time dynamics of 2D Ising model with three spin interactions in one direction and estimate the critical exponents $z,$ $\theta,$ $\beta$ and $\nu$. Taking properly into account the symmetry of the Hamiltonian we obtain results completely different from those obtained by Wang et al.. For the dynamic exponent $z$ our result coincides with that of the 4-state Potts model in two dimensions. In addition, results for the static exponents $\nu$ and $\beta$ agree with previous estimates obtained from finite size scaling combined with conformal invariance. Finally, for the new dynamic exponent $\theta$ we find a negative and close to zero value, a result also expected for the 4-state Potts model according to Okano et al.Comment: 12 pages, 9 figures, corrected Abstract mistypes, corrected equation on page 4 (Parameter Q

Mean-field criticality explained by random matrices theory

How a system initially at infinite temperature responds when suddenly placed at finite temperatures is a way to check the existence of phase transitions. It has been shown in [R. da Silva, IJMPC 2023] that phase transitions are imprinted in the spectra of matrices built from time evolutions of magnetization of spin models. In this paper, we show that this method works very accurately in determining the critical temperature in the mean-field Ising model. We show that for Glauber or Metropolis dynamics, the average eigenvalue has a minimum at the critical temperature, which is corroborated by an inflection at eigenvalue dispersion at this same point. Such transition is governed by a gap in the density of eigenvalues similar to short-range spin systems. We conclude that the thermodynamics of this mean-field system can be described by the fluctuations in the spectra of Wishart matrices which suggests a direct relationship between thermodynamic fluctuations and spectral fluctuations.Comment: 14 pages, 4 figure

Global persistence exponent of the two-dimensional Blume-Capel model

The global persistence exponent $\theta_g$ is calculated for the two-dimensional Blume-Capel model following a quench to the critical point from both disordered states and such with small initial magnetizations. Estimates are obtained for the nonequilibrium critical dynamics on the critical line and at the tricritical point. Ising-like universality is observed along the critical line and a different value $\theta_g =1.080(4)$ is found at the tricritical point.Comment: 7 pages with 3 figure

Universality and scaling study of the critical behavior of the two-dimensional Blume-Capel model in short-time dynamics

In this paper we study the short-time behavior of the Blume-Capel model at the tricritical point as well as along the second order critical line. Dynamic and static exponents are estimated by exploring scaling relations for the magnetization and its moments at early stage of the dynamic evolution. Our estimates for the dynamic exponents, at the tricritical point, are $z= 2.215(2)$ and $\theta= -0.53(2)$.Comment: 12 pages, 9 figure