Speaker
Description
We study two variants of the Blume-Emery-Grifith model with long range mean-field-like interaction and random disorder, described by different Hamiltonians. In one variant the system is uniformly populated by $N$ spins and the disorder is represented by $\textit{i.i.d}$ random variables chosen with probability $p$. In the other one, we consider $N_s\sim Bin(N,p)$ $\textit{strong}$ spins, i.e., spins that interact with a uniform field, while the other $N-N_s$ spins are inert with respect to the field.
Indeed, it is found that the free energy within the two scenarios is unique. The expected energy due to the two Hamiltonians is preserved, leading to an exclusive entropy.
Conflict in the critical behavior between the canonical and the microcanonical ensembles is evident. For example, tricritical points, observed for any amount of disorder in the microcanonical ensemble, emerge only at high disorder, in the canonical ensemble. Constants of motion specifying the microcanonical ensemble, or gaps that open up in the magnetization landscape of the entropy, are other manifestations of disagreement between the two ensembles.
