Probing Criticality Using GMM-Based Potentials
Abstract
Spin models with a given symmetry are easier to sample than scalar theories with the same symmetry on a lattice, as the constrained nature of spin variables enables cheap heat-bath updates. However, this constraint suppresses radial fluctuations, and consequently, spin models cannot be used to study the phenomena of spontaneous symmetry breaking, such as the Higgs phenomenon. To address this, we propose a class of scalar potentials based on Gaussian Mixture Models (GMMs) that are as easy to sample as spin models with a given symmetry. These potentials can be designed to belong to the same universality class as the theory of interest, thereby reproducing its critical properties while enabling efficient sampling. We construct such models for global ℤ2 symmetry, U(1) gauge symmetry, and disordered systems. We also verify by numerical experiment that the case of ℤ2 symmetry in two dimensions lies in the two-dimensional Ising universality class.
Related
- Probing Deconfined Quantum Criticality Point on a Digital Quantum Computer
- Imaginary HTEE: Probing Criticality and Coherence
- Probing metal-insulator criticality with cavity photons
- Probing near-surface potentials with the self-binding threshold of dipolar quantum droplets
- Dynamical large deviations, self-similarity, and criticality
BibTeX
@misc{sharma2026probing,
title = {{Probing Criticality Using GMM-Based Potentials}},
author = {Shashank Sharma and Dipankar Chakrabarti and Vipul Arora},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.02522},
eprint = {2609.02522},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.02522},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Probing Criticality Using GMM-Based Potentials
AU - Shashank Sharma
AU - Dipankar Chakrabarti
AU - Vipul Arora
PY - 2026
DA - 2026/09/02
PB - arXiv
DO - 10.48550/arxiv.2609.02522
UR - https://arxiv.org/abs/2609.02522
AB - Spin models with a given symmetry are easier to sample than scalar theories with the same symmetry on a lattice, as the constrained nature of spin variables enables cheap heat-bath updates. However, this constraint suppresses radial fluctuations, and consequently, spin models cannot be used to study the phenomena of spontaneous symmetry breaking, such as the Higgs phenomenon. To address this, we propose a class of scalar potentials based on Gaussian Mixture Models (GMMs) that are as easy to sample as spin models with a given symmetry. These potentials can be designed to belong to the same universality class as the theory of interest, thereby reproducing its critical properties while enabling efficient sampling. We construct such models for global ℤ_2 symmetry, U(1) gauge symmetry, and disordered systems. We also verify by numerical experiment that the case of ℤ_2 symmetry in two dimensions lies in the two-dimensional Ising universality class.
ER -