Analysis of phase transitions in the mean-field Blume-Emery-Griffiths model

DOI10.1214/105051605000000421zbMath1113.82017arXivmath/0508492OpenAlexW3099395799MaRDI QIDQ2572406

Richard S. Ellis, Peter Tak-Hun Otto, Hugo Touchette

Publication date: 8 November 2005

Published in: The Annals of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0508492

zbMATH Keywords

canonical ensemblemicrocanonical ensembleprobabilistic limit theoremslattice-spin model

Mathematics Subject Classification ID

Central limit and other weak theorems (60F05) Large deviations (60F10) Phase transitions (general) in equilibrium statistical mechanics (82B26) Lattice systems (Ising, dimer, Potts, etc.) and systems on graphs arising in equilibrium statistical mechanics (82B20)

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Large deviation analysis of a droplet model having a Poisson equilibrium distribution ⋮ Multiple critical behavior of probabilistic limit theorems in the neighborhood of a tricritical point ⋮ Nature-inspired algorithms for real-world optimization problems ⋮ Glauber dynamics of 2D Kac-Blume-Capel model and their stochastic PDE limits ⋮ Asymptotic behavior of the finite-size magnetization as a function of the speed of approach to criticality ⋮ Conditional Gaussian fluctuations and refined asymptotics of the spin in the phase-coexistence region ⋮ Gibbs measures of the Blume-Emery-Griffiths model on the Cayley tree ⋮ Absence of first order transition in the random crystal field Blume–Capel model on a fully connected graph ⋮ Lattice gas models with long range interactions ⋮ The aggregate path coupling method for the Potts model on bipartite graph ⋮ Mixing times for the mean-field Blume-Capel model via aggregate path coupling ⋮ Rates of convergence in the Blume-Emery-Griffiths model ⋮ Asymptotic behavior of the magnetization near critical and tricritical points via Ginzburg-Landau polynomials ⋮ Large deviations in discrete-time renewal theory ⋮ The generalized canonical ensemble and its universal equivalence with the microcanonical ensemble ⋮ Large deviations in renewal models of statistical mechanics ⋮ Mixing times for the Swapping Algorithm on the Blume-Emery-Griffiths model

Cites Work

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• The GHS inequality for a large external field
• Complete analysis of phase transitions and ensemble equivalence for the Curie–Weiss–Potts model
• Symmetry breaking and random waves for magnetic systems on a circle
• Limit theorems for sums of dependent random variables occurring in statistical mechanics
• Limit theorems for sums of dependent random variables occurring in statistical mechanics
• Convex Analysis
• Large deviation principles and complete equivalence and nonequivalence results for pure and mixed ensembles

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