Search results for "Critical exponent"
showing 10 items of 141 documents
Monte Carlo study of asymmetric 2D XY model
1997
Employing the Polyakov-Susskind approximation in a field theoretical treatment, the t-J model for strongly correlated electrons in two dimensions has recently been shown to map effectively onto an asymmetric two-dimensional classical XY model. The critical temperature at which charge-spin separation occurs in the t-J model is determined by the location of the phase transitions of this effective model. Here we report results of Monte Carlo simulations which map out the complete phase diagram in the two-dimensional parameter space and also shed some light on the critical behaviour of the transitions.
On multi-scale percolation behaviour of the effective conductivity for the lattice model with interacting particles
2015
Recently, the effective medium approach using 2x2 basic cluster of model lattice sites to predict the conductivity of interacting droplets has been presented by Hattori et al. To make a step aside from pure applications, we have studied earlier a multi-scale percolation, employing any kxk basic cluster for non-interacting particles. Here, with interactions included, we examine in what way they alter the percolation threshold for any cluster case. We found that at a fixed length scale k the interaction reduces the range of shifts of the percolation threshold. To determine the critical concentrations, the simplified model is used. It diminishes the number of local conductivities into two main…
Length-scale-dependent vortex-antivortex unbinding in epitaxialBi2Sr2CaCu2O8+δfilms
1998
The supercurrent transport properties of epitaxial ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8+\mathrm{\ensuremath{\delta}}}$ films in zero applied magnetic field were investigated in a temperature interval of \ensuremath{\approx}20 K below the mean-field critical temperature ${T}_{c0}.$ The modification of the shape of the $I\ensuremath{-}V$ curves observed by varying the temperature was explained in terms of vortex-fluctuation-induced layer decoupling and vortex-antivortex unbinding, revealing a strong probing-length dependence. The change of the effective dimensionality of thermally excited vortices involved in the dissipation process leads to the appearance of …
The Gauge Glass Transition
1993
Results of Monte Carlo simulations in three and four spatial dimensions of a simple model that seems to have the necessary ingredients for disordered type-II superconductor behavior in an external magnetic field are reported. The data suggest that in d = 3 dimensions there is a finite temperature phase transition at T ≈ 0.45 into a truly superconducting vortex glass phase with infinite d.c. conductivity The (effective) correlation length exponent v and the dynamic critical exponent z at this transition are in good agreement with experiments. In d = 4 dimensions the gauge glass transition is located at T ≈ 0.95. It is concluded that the lack of time reversal symmetry in the model places it i…
Surface order in body-centered cubic alloys
1993
Free (100)-surfaces of body-centered cubic binary alloys are studied in a parameter range where the bulk turns from the ordered B2-phase to the disordered A2-phase. A model is chosen that describes iron-aluminium alloys in a fairly realistic way. Mean field treatments and Monte Carlo investigations both show that under certain circumstances the surface remains ordered far above the bulk disordering temperatureT c, though the surface order parameter and the surface susceptibility exhibit a singularity atT c with critical exponents characteristic for the ordinary transition. One finds, that if the surface is nonstoechiometric and different layers are not equivalent with respect to perfect bul…
Continuous Phase Transitions at Surfaces of CuAu Alloy Models — A Monte Carlo Study of Surface Induced Order and Disorder
1996
The influence of surface on phase transitions has found significant attention in recent years, and a number of excellent reviews exists. [1, 2, 3] A variety of complex phenomena occur which are also related to the physics of adsorption and wetting. The scenario of wetting requires three distinct phases, for instance the vacuum, the bulk phase and a third phase intervening in between at equilibrium. In case of surface induced disorder (SID, a film of disordered layers at the surface “wets” the bulk phase as the temperature approaches the bulk transition temperature T c,b. The transition at the surface may be continuous (standard critical wetting phenomena), and, as theoretically investigated…
Surface-induced ordering and disordering in face-centered-cubic alloys: A Monte Carlo study
1996
Using extensive Monte Carlo simulations we have studied phase transitions in a fcc model with antiferromagnetic nearest-neighbor couplings $J$ in the presence of different free surfaces which lead either to surface-induced order or to surface-induced disorder. Our model is a prototype for CuAu-type ordering alloys and shows a strong first-order bulk transition at a temperature $\frac{k{T}_{\mathrm{cb}}}{|J|}=1.738005(50)$. For free (100) surfaces, we find a continuous surface transition at a temperature ${T}_{\mathrm{cs}}g{T}_{\mathrm{cb}}$ exhibiting critical exponents of the two-dimensional Ising model. Surface-induced ordering occurs as the temperature approaches ${T}_{\mathrm{cb}}$ and …
A new boundary-controlled phase transition: Phase separation in an Ising bi-pyramid with competing surface fields
2005
We study phase coexistence of an Ising ferromagnet in a bi-pyramid geometry with a square basal plane of linear extension 2L + 1. Antisymmetric surface fields act on the pyramid surfaces above and below the basal plane. In the limit L → ∞, the magnetisation stays zero at the bulk critical temperature, but becomes discontinuously non-zero at the cone filling critical temperature associated with a single pyramid. Monte Carlo simulations and scaling considerations show that this transition is described by a Landau theory with size-dependent coefficients that give rise to singular critical amplitudes.
Critical behavior of a tumor growth model: directed percolation with a mean-field flavor.
2012
We examine the critical behaviour of a lattice model of tumor growth where supplied nutrients are correlated with the distribution of tumor cells. Our results support the previous report (Ferreira et al., Phys. Rev. E 85, 010901 (2012)), which suggested that the critical behaviour of the model differs from the expected Directed Percolation (DP) universality class. Surprisingly, only some of the critical exponents (beta, alpha, nu_perp, and z) take non-DP values while some others (beta', nu_||, and spreading-dynamics exponents Theta, delta, z') remain very close to their DP counterparts. The obtained exponents satisfy the scaling relations beta=alpha*nu_||, beta'=delta*nu_||, and the general…
Structure of longitudinal chromomagnetic fields in high energy collisions
2014
We compute expectation values of spatial Wilson loops in the forward light cone of high-energy collisions. We consider ensembles of gauge field configurations generated from a classical Gaussian effective action as well as solutions of high-energy renormalization group evolution with fixed and running coupling. The initial fields correspond to a color field condensate exhibiting domain-like structure over distance scales of order the saturation scale. At later times universal scaling emerges at large distances for all ensembles, with a nontrivial critical exponent. Finally, we compare the results for the Wilson loop to the two-point correlator of magnetic fields.