Finite-size scaling and critical exponents in critical relaxation

Finite-size scaling and critical exponents in critical relaxation.

We simulate the critical relaxation process of the two-dimensional Ising model with the initial state both completely disordered or completely ordered. Results of a new method to measure both the dynamic and static critical exponents are reported, based on the finite size scaling for the dynamics at the early time. From the time-dependent Binder cumulant, the dynamical exponent z is extracted i...

Critical percolation in high dimensions: critical exponents, finite size scaling and random walks

Critical Relaxation and Critical Exponents 1

Dynamic relaxation of the XY model and fully frustrated XY model quenched from an initial ordered state to the critical temperature or below is investigated with Monte Carlo methods. Universal power law scaling behaviour is observed. The dynamic critical exponent z and the static exponent η are extracted from the time-dependent Binder cumulant and magnetization. The results are competitive to t...

Finite-size scaling and universality above the upper critical dimensionality.

According to renormalization theory, Ising systems above their upper critical dimensionality du ­ 4 have classical critical behavior and the ratio of magnetization moments Q ­ km2l2ykm4l has the universal value 0.456947 . . .. However, Monte Carlo simulations of d ­ 5 Ising models have been reported which yield strikingly different results, suggesting that the renormalization scenario is incorr...

Critical-point finite-size scaling in the microcanonical ensemble.

We develop a scaling theory for the finite-size critical behavior of the microcanonical entropy (density of states) of a system with a critically divergent heat capacity. The link between the microcanonical entropy and the canonical energy distribution is exploited to establish the former, and corroborate its predicted scaling form, in the case of the 3d Ising universality class. We show that t...