Ferromagnetic phase transition for the spanning-forest model (q \to 0 limit of the Potts model) in three or more dimensions

TL;DR

This paper investigates the ferromagnetic phase transition in the spanning-forest model across three to five dimensions using Monte Carlo simulations, revealing a second-order transition at finite critical points and estimating critical exponents.

Contribution

The study provides the first numerical estimates of the critical point and exponents for the spanning-forest model in dimensions three and higher, suggesting an upper critical dimension of six.

Findings

Second-order phase transition at finite critical point in 3D, 4D, 5D

Numerical estimates of critical exponents provided

Conjecture that the upper critical dimension is 6

Abstract

We present Monte Carlo simulations of the spanning-forest model (q \to 0 limit of the ferromagnetic Potts model) in spatial dimensions d=3,4,5. We show that, in contrast to the two-dimensional case, the model has a "ferromagnetic" second-order phase transition at a finite positive value w_c. We present numerical estimates of w_c and of the thermal and magnetic critical exponents. We conjecture that the upper critical dimension is 6.