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University of Massachusetts Amherst
Ginzburg–Landau phenomenology - Second-order phase transition - First-order phase transition - Tricritical point - Scaling theory - Blume–Capel model
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Asymptotic Behavior Of The Magnetization Near Critical And Tricritical Points Via Ginzburg–Landau Polynomials, R Ellis, J Machta, P Otto
Asymptotic Behavior Of The Magnetization Near Critical And Tricritical Points Via Ginzburg–Landau Polynomials, R Ellis, J Machta, P Otto
Physics 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 (β n ,K n ) …