TY - JOUR

T1 - The liquid-gas critical point in 3.3 dimensions

AU - Valls, Oriol T.

AU - Hertz, J. A.

N1 - Copyright:
Copyright 2015 Elsevier B.V., All rights reserved.

PY - 1978

Y1 - 1978

N2 - Liquid-gas phase transitions are usually assumed to belong to the same universality class as Ising magnets. However, in the liquid-gas case, the free-energy expansion contains odd powers of the order parameter. We show in this work that, even though the odd terms are irrelevant near four dimensions, they become relevant at dimensionality dc=(10-5η)33.33. A new, stable, fixed point may appear. We approximately calculate, to order ε′=dc-d, the difference between the critical exponents for this new fixed point and the Ising critical exponents. This difference turns out to be numerically small. We conclude that, even though in three dimensions the liquid-gas and Ising-magnet phase transition do not belong to the same universality class, the effect on the critical exponents is probably too small to be observed.

AB - Liquid-gas phase transitions are usually assumed to belong to the same universality class as Ising magnets. However, in the liquid-gas case, the free-energy expansion contains odd powers of the order parameter. We show in this work that, even though the odd terms are irrelevant near four dimensions, they become relevant at dimensionality dc=(10-5η)33.33. A new, stable, fixed point may appear. We approximately calculate, to order ε′=dc-d, the difference between the critical exponents for this new fixed point and the Ising critical exponents. This difference turns out to be numerically small. We conclude that, even though in three dimensions the liquid-gas and Ising-magnet phase transition do not belong to the same universality class, the effect on the critical exponents is probably too small to be observed.

UR - http://www.scopus.com/inward/record.url?scp=35949037385&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=35949037385&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.18.2367

DO - 10.1103/PhysRevB.18.2367

M3 - Article

AN - SCOPUS:35949037385

VL - 18

SP - 2367

EP - 2376

JO - Physical Review B

JF - Physical Review B

SN - 0163-1829

IS - 5

ER -