Evaporation-condensation transition of the two-dimensional Potts model in the microcanonical ensemble

Nogawa, Tomoaki; Ito, Nobuyasu

doi:10.1103/physreve.84.061107

Cited by 19 publications

(30 citation statements)

References 22 publications

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“…[53][54][55][56][57][58][59][60][61][62][63] Indeed, at this transition, mid-size droplets are suppressed and the energy distribution is bimodal. Furthermore, the specific latent heat, which we find to decrease with system size (Fig.…”

Section: Discussionmentioning

confidence: 99%

“…For finite-volume liquid-vapor systems at phase coexistence, the formation of droplets due to a fixed particle excess above the ambient gas concentration has been extensively investigated, [53][54][55][56][57][58][59][60][61][62][63] often by mapping to the Ising model at fixed magnetization. A sharp transition has been shown to occur, below which the particle excess can be accommo- latent heat scale as V 3/4 .…”

Section: A Equilibrium Propertiesmentioning

confidence: 99%

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Thermodynamics of amyloid formation and the role of intersheet interactions

Irbäck

Wessén

2015

The Journal of Chemical Physics

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Section: Discussionmentioning

confidence: 99%

Section: A Equilibrium Propertiesmentioning

confidence: 99%

Thermodynamics of amyloid formation and the role of intersheet interactions

Irbäck

Wessén

2015

The Journal of Chemical Physics

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“…The C 1 -continuity of s(u) can be easily verified for the mean field Potts model on a complete graph [17]. For finite-dimensional lattices the phase separation mechanism (the nucleation and expansion of droplets [18][19][20][21]) will guarantee a C 1 -continuous entropy profile in the thermodynamic limit. For random graph systems one would naïvely expect u mic to be an inflection point of s(u) [22], which ensures C 1 -continuity.…”

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confidence: 99%

Kinked Entropy and Discontinuous Microcanonical Spontaneous Symmetry Breaking

Zhou

2019

Phys. Rev. Lett.

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Spontaneous symmetry breaking (SSB) in statistical physics is a macroscopic collective phenomenon. For the paradigmatic Q-state Potts model it means a transition from the disordered color-symmetric phase to an ordered phase in which one color dominates. Existing mean field theories imply that SSB in the microcanonical statistical ensemble (with energy being the control parameter) should be a continuous process. Here we study microcanonical SSB on the random-graph Potts model, and discover that the entropy is a kinked function of energy. This kink leads to a discontinuous phase transition at certain energy density value, characterized by a jump in the density of the dominant color and a jump in the microcanonical temperature. This discontinuous SSB in random graphs is confirmed by microcanonical Monte Carlo simulations, and it is also observed in bond-diluted finite-size lattice systems.Spontaneous symmetry breaking (SSB) is a fundamental concept of physics and is tightly linked to the origin of mass in particle physics, the emergence of superconductivity in condensed-matter system, and the ferromagnetic phase transition in statistical mechanics, to name just a few eminent examples [1]. In statistical physics a theoretical paradigm for SSB is the Potts model, a simple twobody interaction graphical system in which each vertex has Q discrete color states [2][3][4]. The equilibrium SSB transition of the Potts model in the canonical ensemble, where inverse temperature β is the control parameter, has been extensively investigated (see for some of the recent results). Driven by energy-entropy competitions, this transition is a discontinuous phenomenon when Q is sufficiently large, with the density ρ 1 of the dominant color jumps from 1/Q to a much larger value at the critical inverse temperature β c . To compensate for the extensive loss of entropy, such a discontinuous transition is always accompanied by a discontinuous decrease of the system's energy density u [3, 4].When the system is isolated and cannot exchange energy with the environment (the microcanonincal ensemble [13-16]), it is generally believed that the SSB transition will occur gradually, with the dominant color density ρ 1 deviating from 1/Q continuously at certain critical energy density u mic . Indeed if the microscopic entropy density s(u) is a C 1 -continuous function of energy density u (i.e., both s(u) and its first derivative are continuous), there is no reason to expect a discontinuity of the order parameter ρ 1 . The C 1 -continuity of s(u) can be easily verified for the mean field Potts model on a complete graph [17]. For finite-dimensional lattices the phase separation mechanism (the nucleation and expansion of droplets [18-21]) will guarantee a C 1 -continuous entropy profile in the thermodynamic limit. For random graph systems one would naïvely expect u mic to be an inflection point of s(u) [22], which ensures C 1 -continuity.In this Letter we investigate the microcanonical Potts model on random graphs using the Bethe-Peierls mean field theo...

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“…Nonetheless, there is a series of four discontinuous transitions in the microcanonical ensemble, which introduce barriers between the disordered and ordered phases and increase equilibration times. First, at a length scale dependent energy, e 1 (L) < e d there is a transition corresponding to the condensation of an ordered droplet within a disordered background [3,5,6]. As the system size increases, e 1 (L) approaches e d .…”

Section: Model and Observablesmentioning

confidence: 99%

“…Exponential slowing can be substantially reduced using multi-canonical [1] or Wang-Landau [2,3] methods. A related means for reducing exponential slowing is to simulate the system in the microcanonical ensemble [4] rather than the canonical ensemble.…”

Section: Introductionmentioning

confidence: 99%

Equilibrium microcanonical annealing for first-order phase transitions

Rose

Machta

2019

Phys. Rev. E

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A framework is presented for carrying out simulations of equilibrium systems in the microcanonical ensemble using annealing in an energy ceiling. The framework encompasses an equilibrium version of simulated annealing, population annealing and hybrid algorithms that interpolate between these extremes. These equilibrium, microcanonical annealing algorithms are applied to the thermal firstorder transition in the 20-state, two-dimensional Potts model. All of these algorithms are observed to perform well at the first-order transition though for the system sizes studied here, equilibrium simulated annealing is most efficient. arXiv:1907.07067v1 [cond-mat.stat-mech]

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Evaporation-condensation transition of the two-dimensional Potts model in the microcanonical ensemble

Cited by 19 publications

References 22 publications

Thermodynamics of amyloid formation and the role of intersheet interactions

Thermodynamics of amyloid formation and the role of intersheet interactions

Kinked Entropy and Discontinuous Microcanonical Spontaneous Symmetry Breaking

Equilibrium microcanonical annealing for first-order phase transitions

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