Precise determination of critical exponents and equation of state by field theory methods

TL;DR

This paper reviews field theory methods, especially renormalized phi^4_3 quantum field theory, to precisely determine critical exponents and the equation of state for models like the N-vector and 3D Ising, advancing understanding of phase transitions.

Contribution

It presents a detailed review of renormalization group techniques applied to quantum field theory for accurate critical phenomena predictions, improving non-perturbative results.

Findings

Precise critical exponents for N-vector model

Accurate equation of state for 3D Ising model

Field theory methods achieve high-precision non-perturbative results

Abstract

Renormalization group, and in particular its Quantum Field Theory implementation has provided us with essential tools for the description of the phase transitions and critical phenomena beyond mean field theory. We therefore review the methods, based on renormalized phi^4_3 quantum field theory and renormalization group, which have led to a precise determination of critical exponents of the N-vector model (R. Guida and J. Zinn-Justin, J. Phys. A31 (1998) 8103. cond-mat/9803240). and of the equation of state of the 3D Ising model (R. Guida and J. Zinn-Justin, Nucl. Phys. B489 [FS] (1997) 626, hep-th/9610223.). These results are among the most precise available probing field theory in a non-perturbative regime.