Critical Exponents for Long-Range Interactions. II

Ambiguities in estimates of critical exponents for long-range dependent processes

In this article we show that the Hurst parameter and a well-known wavelet estimator fail to distinguish on/off models with substantially different distributions of on-times. We identify the problem as arising when standard power spectrum techniques, which are well-defined for commonly considered processes, are applied to processes with extremely heavy tailed on-times. We provide an elementary m...

Classical critical behavior of spin models with long-range interactions

We present the results of extensive Monte Carlo simulations of Ising models with algebraically decaying ferromagnetic interactions in the regime where classical critical behavior is expected for these systems. We corroborate the values for the exponents predicted by renormalization theory for systems in one, two, and three dimensions and accurately observe the predicted logarithmic corrections ...

Boundary between long-range and short-range critical behavior in systems with algebraic interactions.

We investigate phase transitions of two-dimensional Ising models with power-law interactions, using an efficient Monte Carlo algorithm. For slow decay, the transition is of the mean-field type; for fast decay, it belongs to the short-range Ising universality class. We focus on the intermediate range, where the critical exponents depend continuously on the power law. We find that the boundary wi...

Long - range enhancer - promoter interactions :

Dynamic critical exponents of the Ising model with multispin interactions

We revisit the short-time dynamics of 2D Ising model with three spin interactions in one direction and estimate the critical exponents z, θ, β and ν. Taking properly into account the symmetry of the Hamiltonian we obtain results completely different from those obtained by Wang et al.. For the dynamic exponent z our result coincides with that of the 4-state Potts model in two dimensions. In addi...