The renormalisation group and global G×G' theories about four dimensions

R. D. Pisarski; D. L. Stein

doi:10.1088/0305-4470/14/12/027

The renormalisation group and global G×G' theories about four dimensions

R. D. Pisarski, D. L. Stein

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Abstract

The critical behaviour of linear Phi ⁴ models with global symmetry O(N)*O(M) and U(N)*U(M) is studied at one-loop order in 4- epsilon dimensions. Applications to physical systems include achiral and chiral double-strand polymers, when N=M=0. There exist infrared stables fixed points only if N and M are sufficiently small. Some special cases of interest include (1) O(-2)*O(1) and U(-1)*U(1) which have classical exponents, (2) O(1)*O(1) and O(-2)*O(-2) (for example) which exhibit a 'merging' of critical exponents, (3) M finite, N to infinity which is also calculable in a 1/N expansion.

Original language	English (US)
Article number	027
Pages (from-to)	3341-3355
Number of pages	15
Journal	Journal of Physics A: Mathematical and General
Volume	14
Issue number	12
DOIs	https://doi.org/10.1088/0305-4470/14/12/027
State	Published - 1981

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics
General Physics and Astronomy

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abstract = "The critical behaviour of linear Phi 4 models with global symmetry O(N)*O(M) and U(N)*U(M) is studied at one-loop order in 4- epsilon dimensions. Applications to physical systems include achiral and chiral double-strand polymers, when N=M=0. There exist infrared stables fixed points only if N and M are sufficiently small. Some special cases of interest include (1) O(-2)*O(1) and U(-1)*U(1) which have classical exponents, (2) O(1)*O(1) and O(-2)*O(-2) (for example) which exhibit a 'merging' of critical exponents, (3) M finite, N to infinity which is also calculable in a 1/N expansion.",

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AB - The critical behaviour of linear Phi 4 models with global symmetry O(N)*O(M) and U(N)*U(M) is studied at one-loop order in 4- epsilon dimensions. Applications to physical systems include achiral and chiral double-strand polymers, when N=M=0. There exist infrared stables fixed points only if N and M are sufficiently small. Some special cases of interest include (1) O(-2)*O(1) and U(-1)*U(1) which have classical exponents, (2) O(1)*O(1) and O(-2)*O(-2) (for example) which exhibit a 'merging' of critical exponents, (3) M finite, N to infinity which is also calculable in a 1/N expansion.

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The renormalisation group and global G×G' theories about four dimensions

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