Equilibriumlike extension of the invaded cluster algorithm

Quenched disorder: demixing thermal and disorder fluctuations

We present a finite-size scaling study of the phase transition in the two-dimensional Potts model modified by random bond disorder, in which the average is taken over quantities calculated at quasicritical temperatures of individual disorder configurations. We used the recently proposed equilibrium-like invaded cluster algorithm, which allows us to examine separately the fluctuations in the thermodynamical ensemble from the fluctuations induced by changing the disorder configuration. We point out the crucial role of the spatial inhomogeneities on all scales for the critical behavior of the system. These inhomogeneities are formed by "dressing" of the disorder via critical correlations and are demonstrated to exist for any system size despite the critical fluctuations in thermodynamical ensemble. Such inhomogeneities were previously not thought to be relevant in disorder-altered classical systems when critical temperature is finite. However, we confirm that only by averaging at quasicritical temperatures of each disorder configuration is the thermal critical exponent y(τ) not obscured by the influence of the aforementioned spatial inhomogeneities.

Inhomogeneities on all scales at a phase transition altered by disorder

We have done a finite-size scaling study of a continuous phase transition altered by the quenched bond disorder, investigating systems at quasicritical temperatures of each disorder realization by using the equilibriumlike invaded cluster algorithm. Our results indicate that in order to access the thermal critical exponent y(τ), it is necessary to average the free energy at quasicritical temperatures of each disorder configuration. Despite the thermal fluctuations on the scale of the system at the transition point, we find that spatial inhomogeneities form in the system and become more pronounced as the size of the system increases. This leads to different exponents describing rescaling of the fluctuations of observables in disorder and thermodynamic ensembles.

Equilibriumlike invaded cluster algorithm: critical exponents and dynamical properties

We present a detailed study of the equilibrium-like invaded cluster algorithm, recently proposed as an extension of the invaded cluster algorithm, designed to drive the system to criticality while still preserving the equilibrium ensemble. We perform extensive simulations on two special cases of the Potts model and examine the precision of critical exponents by including the leading corrections. We show that both thermal and magnetic critical exponents can be obtained with high accuracy compared to the best available results. The choice of the auxiliary parameters of the algorithm is discussed in context of dynamical properties. We also discuss the relation to the Li-Sokal bound for the dynamical exponent z.