Universal amplitude ratios from numerical studies of the three-dimensional O(2) model

Precision calculation of universal amplitude ratios in O(N) universality classes: Derivative expansion results at order O(∂^{4})

In the last few years the derivative expansion of the nonperturbative renormalization group has proven to be a very efficient tool for the precise computation of critical quantities. In particular, recent progress in the understanding of its convergence properties allowed for an estimate of the error bars as well as the precise computation of many critical quantities. In this work we extend previous studies to the computation of several universal amplitude ratios for the critical regime of O(N) models using the derivative expansion of the nonperturbative renormalization group at order O(∂^{4}) for three-dimensional systems.

Thermodynamic Casimir effect in 4He films near Tlambda: Monte Carlo results

The universal finite-size scaling function of the critical Casimir force for the three dimensional XY universality class with Dirichlet boundary conditions is determined using Monte Carlo simulations. The results are in excellent agreement with recent experiments on 4He Films at the superfluid transition and with available theoretical predictions.

Bulk and surface phase transitions in the three-dimensional O4 spin model

We investigate the O(4) spin model on the simple-cubic lattice by means of the Wolff cluster algorithm. Using the toroidal boundary condition, we locate the bulk critical point at coupling K(c) = 0.935 856(2), and determine the bulk thermal magnetic renormalization exponents as y(t) = 1.337 5(15) and y(h) = 2.482 0(2), respectively. The universal ratio Q=m(2)(2)/m(4) is also determined as 0.9142(1). The precision of these estimates significantly improves over that of the existing results. Then, we simulate the critical O(4) model with two open surfaces on which the coupling strength K(1) can be varied. At the ordinary transitions, the surface magnetic exponent is determined as y((o))(h1) = 1.020 2(12). Further, we find a so-called special surface transition at (k) = K(1)/K-1 = 1.258(20). At this point, the surface thermal exponent y(s)(t1) is rather close to zero, and we cannot exclude that the corresponding surface transition is Kosterlitz-Thouless-like. The surface magnetic exponent is y((s))/h1 = 1.816(2).

Surface and bulk transitions in three-dimensional O(n) models

Using Monte Carlo methods and finite-size scaling, we investigate surface criticality in the O(n) models on the simple-cubic lattice with n=1 , 2, and 3, i.e., the Ising, XY , and Heisenberg models. For the critical couplings we find Kc (n=2) =0.454 1659 (10) and Kc (n=3) =0.693 003 (2). We simulate the three models with open surfaces and determine the surface magnetic exponents at the ordinary transition to be y (o)(h1) =0.7374 (15) , 0.781 (2), and 0.813 (2) for n=1 , 2, and 3, respectively. Then we vary the surface coupling K1 and locate the so-called special transition at kappa(c) (n=1) =0.502 14 (8) and kappa(c) (n=2) =0.6222 (3), where kappa= K1 /K-1 . The corresponding surface thermal and magnetic exponents are y (s)(t1) =0.715 (1) and y (s)(h1) =1.636 (1) for the Ising model, and y(s)(t1) =0.608 (4) and y(s)(h1) =1.675 (1) for the XY model. Finite-size corrections with an exponent close to -1/2 occur for both models. Also for the Heisenberg model we find substantial evidence for the existence of a special surface transition.

Density of states of classical spin systems with continuous degrees of freedom

In the last years different studies have revealed the usefulness of a microcanonical analysis of finite systems when dealing with phase transitions. In this approach the quantities of interest are exclusively expressed as derivatives of the entropy S=ln Omega where Omega is the density of states. Obviously, the density of states has to be known with very high accuracy for this kind of analysis. Important progress has been achieved recently in the computation of the density of states of classical systems, as new types of algorithms have been developed. Here we extend one of these methods, originally formulated for systems with discrete degrees of freedom, to systems with continuous degrees of freedom. As an application we compute the density of states of the three-dimensional XY model and demonstrate that critical quantities can directly be determined from the density of states of finite systems in cases where the degrees of freedom take continuous values.

Critical behavior and scaling functions of the three-dimensional O(6) model

We numerically investigate the three-dimensional O(6) model on 12(3) to 120(3) lattices within the critical region at zero magnetic field, as well as at finite magnetic field on the critical isotherm and for several fixed couplings in the broken and the symmetric phase. We obtain from the Binder cumulant at vanishing magnetic field the critical coupling J(c)=1.42865(3). The universal value of the Binder cumulant at this point is g(r)(J(c))=-1.94456(10). At the critical coupling, the critical exponents gamma=1.604(6), beta=0.425(2), and nu=0.818(5) are determined from a finite-size-scaling analysis. Furthermore, we verify predicted effects induced by massless Goldstone modes in the broken phase. The results are well described by the perturbative form of the model's equation of state. Our O(6) result is compared to the corresponding Ising, O(2) and O(4) scaling functions. Finally, we study the finite-size-scaling behavior of the magnetization on the pseudocritical line.