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On first-order phase transitions in microcanonical and canonical non-extensive systems

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  • Ispolatov, I
  • Cohen, E.G.D

Abstract

Two examples of Microcanonical Potts models, two-dimensional nearest neighbor and mean field, are considered via exact enumeration of states and analytical asymptotic methods. In the interval of energies corresponding to a first order phase transition, both of these models exhibit a convex dip in the entropy vs. energy plot and a region with negative specific heat within the dip. It is observed that in the nearest neighbor model the dip flattens and disappears as the lattice size grows, while in the mean field model the dip persists even in the limit of an infinite system. If formal transitions from microcanonical to canonical ensembles and back are performed for an infinite but non-extensive system, the convex dip in the microcanonical entropy plot disappears.

Suggested Citation

  • Ispolatov, I & Cohen, E.G.D, 2001. "On first-order phase transitions in microcanonical and canonical non-extensive systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 295(3), pages 475-487.
    • Handle: RePEc:eee:phsmap:v:295:y:2001:i:3:p:475-487
    DOI: 10.1016/S0378-4371(01)00159-5
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    Cited by:

    1. Moreno, Felipe & Davis, Sergio & Loyola, Claudia & Peralta, Joaquín, 2018. "Ordered metastable states in the Potts model and their connection with the superheated solid state," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 361-368.
    2. Barré, Julien & Gonçalves, Bruno, 2007. "Ensemble inequivalence in random graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 386(1), pages 212-218.
    3. Montecinos, Alejandra & Loyola, Claudia & Peralta, Joaquín & Davis, Sergio, 2021. "Microcanonical potential energy fluctuations and configurational density of states for nanoscale systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 562(C).
    4. Casetti, Lapo & Kastner, Michael, 2007. "Partial equivalence of statistical ensembles and kinetic energy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 384(2), pages 318-334.
    5. Davis, Sergio, 2022. "A classification of nonequilibrium steady states based on temperature correlations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 608(P1).
    6. Rodrigues, B.B. & Rocha, J.C.S. & Costa, B.V., 2022. "Phase diagram of flexible polymers with quenched disordered charged monomers," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 604(C).

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