TY - JOUR

T1 - Renormalization-group analysis of lifshitz tricritical behavior

AU - Aharony, Amnon

AU - Domany, Eytan

AU - Hornreich, R. M.

PY - 1987

Y1 - 1987

N2 - A renormalization-group analysis of critical behavior near a Lifshitz tricritical point (LTP) is presented, with emphasis on the role played by new, momentum-dependent quartic terms. These result in new stable fixed points which determine the critical behavior. For some values of n (the number of order-parameter components) and m (the dimensionality of the softsubspace, characterized by quartic momentum-dependent inverse correlation functions), the renormalization-group recursion relations have two stable and accessible fixed points. However, one of these can never be reached in practice, due to a thermodynamic instability which results in a first-order phase transition. For m=d-1, one of the fixed points describes the critical dynamics of the usual n-vector spin model in (d-1) dimensions. This dynamic fixed point also characterizes LTP behavior for large n and n=1. In all other cases, the LTP has new exponents, which are not related to the dynamic model. Our results may be relevant to Lifshitz tricritical behavior in RbCaF3 and in some liquid-crystal systems.

AB - A renormalization-group analysis of critical behavior near a Lifshitz tricritical point (LTP) is presented, with emphasis on the role played by new, momentum-dependent quartic terms. These result in new stable fixed points which determine the critical behavior. For some values of n (the number of order-parameter components) and m (the dimensionality of the softsubspace, characterized by quartic momentum-dependent inverse correlation functions), the renormalization-group recursion relations have two stable and accessible fixed points. However, one of these can never be reached in practice, due to a thermodynamic instability which results in a first-order phase transition. For m=d-1, one of the fixed points describes the critical dynamics of the usual n-vector spin model in (d-1) dimensions. This dynamic fixed point also characterizes LTP behavior for large n and n=1. In all other cases, the LTP has new exponents, which are not related to the dynamic model. Our results may be relevant to Lifshitz tricritical behavior in RbCaF3 and in some liquid-crystal systems.

UR - http://www.scopus.com/inward/record.url?scp=0039164455&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.36.2006

DO - 10.1103/PhysRevB.36.2006

M3 - מאמר

AN - SCOPUS:0039164455

VL - 36

SP - 2006

EP - 2014

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

SN - 1098-0121

IS - 4

ER -