After a brief general overview of Monte Carlo computer simulations in statistical physics, special emphasis is placed on applications to phase transitions and critical phenomena. Here, standard simulations employing local update algorithms are severely hampered by the problem of critical slowing...

Conformal field theory (CFT) predicts universal relations between scaling amplitudes and scaling dimensions for two-dimensional systems on infinite length cylinders, which hold true even independent of the model under consideration. We discuss different possible generalizations of such laws to...

Although there is now a good measure of agreement between Monte Carlo and high-temperature series expansion estimates for Ising (n = 1) models, published results for the critical temperature from series expansions up to 12th order for the three-dimensional classical Heisenberg (n = 3) and XY (n...

Under certain conditions phase transitions in systems with quenched disorder are expected to exhibit a different behaviour than in the corresponding pure system. Here we discuss a series of Monte Carlo studies of a special type of such disordered systems, namely spin models defined on quenched,...

We derive high-temperature series expansions for the free energy and susceptibility of the two-dimensional random-bond Ising model with a symmetric bimodal distribution of two positive coupling strengths J1 and J2 and study the influence of the quenched, random bond-disorder on the critical...

Canonical Monte Carlo simulations of disordered systems like spin glasses and systems undergoing first-order phase transitions are severely hampered by rare event states which lead to exponentially diverging autocorrelation times with increasing system size and hence to exponentially large...

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...