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Full-Text Articles in Physical Sciences and Mathematics
Asymptotic Behavior Of The Magnetization Near Critical And Tricritical Points Via Ginzburg-Landau Polynomials, Rs Ellis, J Machta, Pth Otto
Asymptotic Behavior Of The Magnetization Near Critical And Tricritical Points Via Ginzburg-Landau Polynomials, Rs Ellis, J Machta, Pth Otto
Mathematics and Statistics Department Faculty Publication Series
The purpose of this paper is to prove connections among the asymptotic behavior of the magnetization, the structure of the phase transitions, and a class of polynomials that we call the Ginzburg–Landau polynomials. The model under study is a mean-field version of a lattice spin model due to Blume and Capel. It is defined by a probability distribution that depends on the parameters β and K, which represent, respectively, the inverse temperature and the interaction strength. Our main focus is on the asymptotic behavior of the magnetization m(β n ,K n ) for appropriate sequences ( …
Multiple Critical Behavior Of Probabilistic Limit Theorems In The Neighborhood Of A Tricritical Point, M Costeniuc, Rs Ellis, Pth Otto
Multiple Critical Behavior Of Probabilistic Limit Theorems In The Neighborhood Of A Tricritical Point, M Costeniuc, Rs Ellis, Pth Otto
Mathematics and Statistics Department Faculty Publication Series
We derive probabilistic limit theorems that reveal the intricate structure of the phase transitions in a mean-field version of the Blume–Emery–Griffiths model [Phys. Rev. A 4 (1971) 1071–1077]. These probabilistic limit theorems consist of scaling limits for the total spin and moderate deviation principles (MDPs) for the total spin. The model under study is defined by a probability distribution that depends on the parameters n, β, and K, which represent, respectively, the number of spins, the inverse temperature, and the interaction strength. The intricate structure of the phase transitions is revealed by the existence of 18 scaling …
Analysis Of Phase Transitions In The Mean-Field Blume-Emery-Griffiths Model, Rs Ellis, Pt Otto, H Touchette
Analysis Of Phase Transitions In The Mean-Field Blume-Emery-Griffiths Model, Rs Ellis, Pt Otto, H Touchette
Mathematics and Statistics Department Faculty Publication Series
In this paper we give a complete analysis of the phase transitions in the mean-field Blume-Emery-Griffiths lattice-spin model with respect to the canonical ensemble, showing both a second-order, continuous phase transition and a first-order, discontinuous phase transition for appropriate values of the thermodynamic parameters that define the model. These phase transitions are analyzed both in terms of the empirical measure and the spin per site by studying bifurcation phenomena of the corresponding sets of canonical equilibrium macrostates, which are defined via large deviation principles. Analogous phase transitions with respect to the microcanonical ensemble are also studied via a combination of …