Phase separation and correlations between itinerant defects in a constrained Blume-Capel model using Grassmann techniques
Abstract
We study the Blume-Capel model with a fixed concentration of spin-zero states, modeled as classical particles or defects moving in a fluctuating two-dimensional magnetic medium made of Ising spins. These defects can diffuse on the lattice either by exchanging positions with a neighboring or distant spin if these processes are energetically favorable. We use a fermionic representation of the theory in order to transform the partition function into a multiple integral over Grassmann variables. This model of annealed disorder can be described by a Grassmannian action containing quartic interaction terms between the defects. Under the assumption that the quartic term does not contribute to the physics at long distances, we study the critical behavior of this system as well as the entropy, specific heat, and residual correlation functions, which are evaluated within this formalism and compared with Monte Carlo simulations. In addition to the peak associated with the altered spin critical regime, the specific heat exhibits another peak at a lower temperature. This corresponds to the condensation or crystallization of the defects as they form a single giant cluster in the ground state. This finding is substantiated by the analysis of the entropy. The Grassmannian formalism allows for a practical and direct computation of the correlation functions between defects. We found that the correlations are strongly attractive at short distances in the low temperature regime and over a broader range of distances near the spin critical regime, and slightly repulsive at large distances.
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BibTeX
@article{fortin2026phase,
title = {{Phase separation and correlations between itinerant defects in a constrained Blume-Capel model using Grassmann techniques}},
author = {Jean-Yves Fortin},
journal = {Physica A: Statistical Mechanics and its Applications},
year = {2026},
month = sep,
doi = {10.1016/j.physa.2026.132023},
url = {https://hal.science/hal-04408010v2},
note = {CC BY 4.0},
}
RIS
TY - JOUR
TI - Phase separation and correlations between itinerant defects in a constrained Blume-Capel model using Grassmann techniques
AU - Jean-Yves Fortin
PY - 2026
DA - 2026/09/08
JO - Physica A: Statistical Mechanics and its Applications
DO - 10.1016/j.physa.2026.132023
UR - https://hal.science/hal-04408010v2
AB - We study the Blume-Capel model with a fixed concentration of spin-zero states, modeled as classical particles or defects moving in a fluctuating two-dimensional magnetic medium made of Ising spins. These defects can diffuse on the lattice either by exchanging positions with a neighboring or distant spin if these processes are energetically favorable. We use a fermionic representation of the theory in order to transform the partition function into a multiple integral over Grassmann variables. This model of annealed disorder can be described by a Grassmannian action containing quartic interaction terms between the defects. Under the assumption that the quartic term does not contribute to the physics at long distances, we study the critical behavior of this system as well as the entropy, specific heat, and residual correlation functions, which are evaluated within this formalism and compared with Monte Carlo simulations. In addition to the peak associated with the altered spin critical regime, the specific heat exhibits another peak at a lower temperature. This corresponds to the condensation or crystallization of the defects as they form a single giant cluster in the ground state. This finding is substantiated by the analysis of the entropy. The Grassmannian formalism allows for a practical and direct computation of the correlation functions between defects. We found that the correlations are strongly attractive at short distances in the low temperature regime and over a broader range of distances near the spin critical regime, and slightly repulsive at large distances.
SN - 0378-4371
SN - 0378-4371
ER -