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Updated: Jul 2, 2025

Tissue Triage and Freezing for Models of Skeletal Muscle Disease
Published on: July 15, 2014
Ising model for the freezing transition
Jacobo Troncoso1, Claudio A Cerdeiriña1
1Instituto de Física e Ciencias Aeroespaciais da Universidade de Vigo and Unidad MSMN Asociada al CSIC por el IQF Blas Cabrera, Ourense 32004, Spain.
Abstract:
We introduce a three-state Ising model with entropy-volume coupling suitably incorporating a packing mechanism into a lattice gas with no attractive interactions. On working in a great grand canonical ensemble in which the energy, volume, and number of particles are all allowed to fluctuate simultaneously, the model's mean-field solutions illuminate a strictly first-order transition akin to hard-sphere freezing while describing the thermodynamics of solid and fluid phases. Further implementation of attractive interactions in a natural way allows every aspect of the phase diagram of a simple substance to be reproduced, thereby accomplishing the van der Waals picture of the states of matter from first principles of statistical mechanics. This fairly accurate qualitative description plausibly renders mean-field theory a reasonable approach for freezing in three dimensions. At the same time, our mean-field treatment itself suggests freezing to persist in infinitely many dimensions, as advanced from recent simulations [Charbonneau et al., Eur. Phys. J. E 44, 101 (2021)10.1140/epje/s10189-021-00104-y].
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