23 research outputs found
Global persistence exponent of the double-exchange model
We obtained the global persistence exponent for a continuous spin
model on the simple cubic lattice with double-exchange interaction by using two
different methods. First, we estimated the exponent by following the
time evolution of probability that the order parameter of the model does
not change its sign up to time . Afterwards,
that exponent was estimated through the scaling collapse of the universal
function 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 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
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 oxygen atoms ranging from 4 to 225.
Finally, from a linear regression of the transfer matrix results, we obtain an
estimate for the case 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 and are obtained using short-time Monte Carlo
simulations. We also estimate the static critical exponents and
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
and . 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 our result coincides with that of the
4-state Potts model in two dimensions. In addition, results for the static
exponents and agree with previous estimates obtained from finite
size scaling combined with conformal invariance. Finally, for the new dynamic
exponent 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 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 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 and .Comment: 12 pages, 9 figure