Microscopic theory of phase transitions in a critical region

被引：13

作者：

Kocharovsky, Vitaly V. ^{[1
,2
]}

Kocharovsky, Vladimir V. ^{[2
,3
]}

机构：

[1] Texas A&M Univ, Dept Phys & Astron, College Stn, TX 77843 USA

[2] Russian Acad Sci, Inst Appl Phys, Nizhnii Novgorod 603950, Russia

[3] Lobachevsky State Univ Nizhny Novgorod, Nizhnii Novgorod 603950, Russia

来源：

PHYSICA SCRIPTA | 2015年 / 90卷 / 10期

关键词：

critical phenomena; mesoscopic system; phase transitions; spontaneous symmetry breaking; microscopic theory; Bose-Einstein condensation; ferromagnetism; BOSE-EINSTEIN CONDENSATION; NONPOLYNOMIAL AVERAGES; MODEL; EQUIVALENCE; BEHAVIOR;

D O I：

10.1088/0031-8949/90/10/108002

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

The problem of finding a microscopic theory of phase transitions across a critical point is a central unsolved problem in theoretical physics. We find a general solution to that problem and present it here for the cases of Bose-Einstein condensation (BEC) in an interacting gas and ferromagnetism in a lattice of spins, interacting via a Heisenberg or Ising Hamiltonian. For BEC, we present the exact, valid for the entire critical region, equations for the Green's functions and order parameter, that is a critical-region extension of the Beliaev-Popov and Gross-Pitaevskii equations. For the magnetic phase transition, we find an exact theory in terms of constrained bosons in a lattice and obtain similar equations for the Green's functions and order parameter. In particular, we outline an exact solution for the three-dimensional Ising model.

引用

页数：23

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