1,720,963 research outputs found
Universality of the glassy transitions in the two-dimensional +/- J Ising model
No full textWe investigate the zero-temperature glassy transitions in the square-lattice +/- J Ising model, with bond distribution P(J(xy)) = p delta(J(xy)-J) + (1-p)delta(J(xy)+J); p=1 and p=1/2 correspond to the pure Ising model and to the Ising spin glass with symmetric bimodal distribution, respectively. We present finite-temperature Monte Carlo simulations at p=4/5, which is close to the low-temperature paramagnetic-ferromagnetic transition line located at p approximate to 0.89, and at p=1/2. Their comparison provides a strong evidence that the glassy critical behavior that occurs for 1-p(0)<p<p(0), p(0)approximate to 0.897, is universal, i.e., independent of p. Moreover, we show that glassy and magnetic modes are not coupled at the multicritical zero-temperature point where the paramagnetic-ferromagnetic transition line and the T=0 glassy transition line meet. On the theoretical side we discuss the validity of finite-size scaling in glassy systems with a zero-temperature transition and a discrete Hamiltonian spectrum. Because of a freezing phenomenon which occurs in a finite volume at sufficiently low temperatures, the standard finite-size scaling limit in terms of TL(1/v) does not exist; the renormalization-group invariant quantity xi/L should be used instead as basic variable
Strong-Disorder Paramagnetic-Ferromagnetic Fixed Point in the Square-Lattice +/- J Ising Model
No full textWe consider the random-bond +/- J Ising model on a square lattice as a function of the temperature T and of the disorder parameter p (p=1 corresponds to the pure Ising model). We investigate the critical behavior along the paramagnetic-ferromagnetic transition line at low temperatures, below the temperature of the multicritical Nishimori point at T (*)=0.9527(1), p (*)=0.89083(3). We present finite-size scaling analyses of Monte Carlo results at two temperature values, Ta parts per thousand 0.645 and T=0.5. The results show that the paramagnetic-ferromagnetic transition line is reentrant for T T (*). Our results for the critical exponents are consistent with the hyperscaling relation 2 beta/nu-eta=d-2=0
Universal dependence on disorder of two-dimensional randomly diluted and random-bond +/- J Ising models
No full textWe consider the two-dimensional randomly site diluted Ising model and the random-bond +/- J Ising model (also called the Edwards-Anderson model), and study their critical behavior at the paramagnetic-ferromagnetic transition. The critical behavior of thermodynamic quantities can be derived from a set of renormalization-group equations, in which disorder is a marginally irrelevant perturbation at the two-dimensional Ising fixed point. We discuss their solutions, focusing in particular on the universality of the logarithmic corrections arising from the presence of disorder. Then, we present a finite-size scaling analysis of high-statistics Monte Carlo simulations. The numerical results confirm the renormalization-group predictions, and in particular the universality of the logarithmic corrections to the Ising behavior due to quenched dilution
The universality class of 3D site-diluted and bond-diluted Ising systems
No full textWe present a finite-size scaling analysis of high-statistics Monte Carlo simulations of the three-dimensional randomly site-diluted and bond-diluted Ising model. The critical behaviour of these systems is affected by slowly decaying scaling corrections which make the accurate determination of their universal asymptotic behaviour quite hard, requiring an effective control of the scaling corrections. For this purpose we exploit improved Hamiltonians, for which the leading scaling corrections are suppressed for any thermodynamic quantity, and improved observables, for which the leading scaling corrections are suppressed for any model belonging to the same universality class. The results of the finite-size scaling analysis provide strong numerical evidence that phase transitions in three-dimensional randomly site-diluted and bond-diluted Ising models belong to the same randomly dilute Ising universality class. We obtain accurate estimates of the critical exponents nu = 0.683(2), eta = 0.036(1), alpha = - 0.049(6), gamma = 1.341(4), beta = 0.354(1), delta = 4.792(6), and of the leading and next-to-leading correction-to-scaling exponents, omega = 0.33(3) and omega(2) = 0.82(8)
The 3-D O(4) universality class and the phase transition in two-flavor QCD
No full textWe determine the critical equation of state of the three-dimensional O(4)
universality class. We first consider the small-field expansion of the
effective potential (Helmholtz free energy). Then, we apply a systematic
approximation scheme based on polynomial parametric representations that are
valid in the whole critical regime, satisfy the correct analytic properties
(Griffiths' analyticity), take into account the Goldstone singularities at the
coexistence curve, and match the small-field expansion of the effective
potential. From the approximate representations of the equation of state, we
obtain estimates of several universal amplitude ratios.
The three-dimensional O(4) universality class is expected to describe the
finite-temperature chiral transition of quantum chromodynamics with two light
flavors. Within this picture, the O(4) critical equation of state relates the
reduced temperature, the quark masses, and the condensates around T_c in the
limit of vanishing quark masses
The 3D +-J Ising model at the ferromagnetic transition line
No full textWe study the critical behavior of the three-dimensional Ising model
[with a random-exchange probability ] at the transition line between the paramagnetic and
ferromagnetic phase, which extends from to a multicritical (Nishimori)
point at . By a finite-size scaling analysis of Monte Carlo
simulations at various values of in the region , we provide strong
numerical evidence that the critical behavior along the ferromagnetic
transition line belongs to the same universality class as the three-dimensional
randomly-dilute Ising model. We obtain the results and
for the critical exponents, which are consistent with the
estimates and at the transition of
randomly-dilute Ising models
Magnetic-glassy multicritical behavior of the three-dimensional +- J Ising model
No full textWe consider the three-dimensional model defined on a simple cubic
lattice and study its behavior close to the multicritical Nishimori point where
the paramagnetic-ferromagnetic, the paramagnetic-glassy, and the
ferromagnetic-glassy transition lines meet in the T-p phase diagram (p
characterizes the disorder distribution and gives the fraction of ferromagnetic
bonds). For this purpose we perform Monte Carlo simulations on cubic lattices
of size and a finite-size scaling analysis of the numerical results.
The magnetic-glassy multicritical point is found at , along the
Nishimori line given by . We determine the
renormalization-group dimensions of the operators that control the
renormalization-group flow close to the multicritical point, ,
, and the susceptibility exponent . The
temperature and crossover exponents are and , respectively. We also investigate the model-A dynamics, obtaining
the dynamic critical exponent
Critical behavior of the random-anisotropy model in the strong-anisotropy limit
No full textWe investigate the nature of the critical behavior of the random-anisotropy
Heisenberg model (RAM), which describes a magnetic system with random uniaxial
single-site anisotropy, such as some amorphous alloys of rare earths and
transition metals. In particular, we consider the strong-anisotropy limit
(SRAM), in which the Hamiltonian can be rewritten as the one of an Ising
spin-glass model with correlated bond disorder. We perform Monte Carlo
simulations of the SRAM on simple cubic L^3 lattices, up to L=30, measuring
correlation functions of the replica-replica overlap, which is the order
parameter at a glass transition. The corresponding results show critical
behavior and finite-size scaling. They provide evidence of a finite-temperature
continuous transition with critical exponents and
. These results are close to the corresponding estimates that
have been obtained in the usual Ising spin-glass model with uncorrelated bond
disorder, suggesting that the two models belong to the same universality class.
We also determine the leading correction-to-scaling exponent finding
Finite-size scaling in two-dimensional Ising spin glass models
No full textWe study the finite-size behavior of two-dimensional spin-glass models. We
consider the +-J model for two different values of the probability of the
antiferromagnetic bonds and the model with Gaussian distributed couplings. The
analysis of renormalization-group invariant quantities, the overlap
susceptibility, and the two-point correlation function confirms that they
belong to the same universality class. We analyze in detail the standard
finite-size scaling limit in terms of TL^(1/nu) in the +-J model. We find that
it holds asymptotically. This result is consistent with the low-temperature
crossover scenario in which the crossover temperature, which separates the
universal high-temperature region from the discrete low-temperature regime,
scales as T_c(L) ~ L^(-theta_S) with theta_S \approx 0.5
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