Crossover exponent in O(N) phi^4 theory at O(1/N^2)

TL;DR

This paper calculates the crossover exponent in O(N) phi^4 theory at O(1/N^2), providing new high-order insights and resummation estimates relevant for understanding phase transitions across dimensions.

Contribution

It extends the large N expansion of the crossover exponent to O(1/N^2) and compares it with perturbative results, offering new five-loop structure insights.

Findings

Epsilon expansion matches known perturbative results up to O(epsilon^4)

Provides estimates of crossover exponents for various N in three dimensions

Offers new structural understanding of five-loop exponents

Abstract

The critical exponent phi_c, derived from the anomalous dimension of the bilinear operator responsible for crossover behaviour in O(N) phi^4 theory, is calculated at O(1/N^2) in a large N expansion in arbitrary space-time dimension d = 4 - 2 epsilon. Its epsilon expansion agrees with the known O(epsilon^4) perturbative expansion and new information on the structure of the five loop exponent is provided. Estimates of phi_c and the related crossover exponents beta_c and gamma_c, using Pade-Borel resummation, are provided for a range of N in three dimensions.