Dresden 2026 – scientific programme

Parts | Days | Selection | Search | Updates | Downloads | Help

DY: Fachverband Dynamik und Statistische Physik

DY 47: Statistical Physics: General I

DY 47.2: Talk

Thursday, March 12, 2026, 09:45–10:00, ZEU/0114

Ensemble dependence of the critical behavior of a system with long range interaction and quenched randomness — •Nir Schreiber, Reuven Cohen, and Simi Haber — Department of Mathematics, Bar Ilan University, Ramat Gan, Israel 5290002

A system with long range interaction (LRI) is usually non-additive. In other words, such a system with volume V and energy E, cannot be divided into two subsystems with energies E₁,E₂ , where E = E₁ + E₂ + o(V).

The canonical and the microcanonical ensembles are expected to be equivalent when describing additive systems. Conversely, non-additivity may result in peculiar microcanonical phenomena that are not observed in the canonical ensemble, such as negative specific heat or the presence of microstates that are inaccessible to the system, leading to breaking of ergodicity.

The Blume-Emery-Griffiths (BEG) model with mean-field-like interaction is a simple example of a model with LRI. We employ that model to demonstrate inequivalence of the two ensembles, without interfering with the interaction content. Specifically, we consider a hybrid system governed by the BEG Hamiltonian, where the spins are randomly quenched such that some of them are “pure” Ising and the others admit the BEG states. It is found, by varying the concentration of the Ising spins while keeping the parameters of the Hamiltonian fixed, that the model displays different canonical and microcanonical phase portraits in concentration-temperature plain. Indications that these portraits are rich and rather unusual are provided.

Keywords: Critical phenomena; Phase transitions