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First order phase transitions in nonlinear vector and lattice gauge models.(Applications of Renormalization Group Methods in Mathematical Sciences)

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First

order

phase

transitions in

nonlinear

vector

and

lattice

gauge

models.

A.C.D.van.Enter (workwith S.B.Shlosman)

Center

for Theoretical Physics Rijksuniversiteit Groningen

Groningen, Netherlands

Abstract

Inthis contribution we discuss a number of results which seem to violate thenotionof universality, atleastas formulated inthenaiveversion wherethe dimension, the spontaneously broken symmetry and the short-range nature

of the interaction should imply the nature of the transition. We show in

particularthat various$\mathrm{d}$-dimensional SO(n)-invariantferromagneticn-vector

modelswith $\mathrm{n}$and

$\mathrm{d}$atleast 2 have first-ordertransitions inthetemperature

variable.

These models are nonlinear in the sense that the interaction is some

function of the inner product between neighboring spin vectors which has

theform ofa deep and narrow well.

Similar results hold for liquidcrystal modelsof Lebwohl-Lashertypeand in lattice

gauge

models in $\mathrm{d}=3$ or more. Both the proof and the intuition behind it arebased on a similarity with high-state Potts models.

数理解析研究所講究録

参照

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