Ensemble-dependent effect of disorder on multicritical points in a system with long-range interactions
Abstract
We introduce two variants of the Blume--Emery--Griffiths model with long-range, mean-field-like interactions and quenched disorder. Although the two variants are described by different Hamiltonians, they yield the same free energy. Moreover, both Hamiltonians lead to the same average energy and hence to the same microcanonical entropy. The canonical and microcanonical phase boundaries differ markedly, and so does the multicritical behaviour of the two ensembles. In the microcanonical ensemble, tricritical points appear for any fraction of active spins, whereas in the canonical ensemble they emerge only when this fraction is sufficiently large. At lower fractions, canonical critical endpoints arise instead. We also report the formation of gaps in the entropy as a function of magnetization, another manifestation of ensemble inequivalence.
Related
- Numerical Study of Stability of Clean Critical Points across Aperiodic, Topological, and Uncorrelated Disorder
- Death by mutants: unusual multicritical dynamics in a two-species model for absorbing state transitions
- Ensemble-dependent condensate statistics and correlations in an ideal Bose gas
- Can a Spin Liquid State Persist as the Ground State in the Presence of Competing Interactions and Disorder?
- Static and Ensemble-Dependent Thermodynamics of the Strain-Induced Parity Anomaly in Gapped Graphene
BibTeX
@misc{schreiber2026ensembledependent,
title = {{Ensemble-dependent effect of disorder on multicritical points in a system with long-range interactions}},
author = {Nir Schreiber and Reuven Cohen},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.39929},
eprint = {2610.39929},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.39929},
}
RIS
TY - UNPB
TI - Ensemble-dependent effect of disorder on multicritical points in a system with long-range interactions
AU - Nir Schreiber
AU - Reuven Cohen
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.39929
UR - https://arxiv.org/abs/2610.39929
AB - We introduce two variants of the Blume--Emery--Griffiths model with long-range, mean-field-like interactions and quenched disorder. Although the two variants are described by different Hamiltonians, they yield the same free energy. Moreover, both Hamiltonians lead to the same average energy and hence to the same microcanonical entropy. The canonical and microcanonical phase boundaries differ markedly, and so does the multicritical behaviour of the two ensembles. In the microcanonical ensemble, tricritical points appear for any fraction of active spins, whereas in the canonical ensemble they emerge only when this fraction is sufficiently large. At lower fractions, canonical critical endpoints arise instead. We also report the formation of gaps in the entropy as a function of magnetization, another manifestation of ensemble inequivalence.
ER -