On the Finite-Temperature Generalization of the C-theorem and the Interplay between Classical and Quantum Fluctuations

TL;DR

This paper investigates the finite-temperature behavior of the C-function in a solvable lattice model across different dimensions, revealing how classical and quantum fluctuations influence its monotonicity and critical phenomena.

Contribution

It provides the first exact derivation of the finite-temperature C-function's scaling behavior in a d-dimensional lattice model within the same universality class as the quantum nonlinear O(n) sigma model.

Findings

Derived scaling functions of C for d=1, 2, 4.

Identified regions where C is monotonically increasing.

Modified finite-size scaling theory for d=4.

Abstract

The behavior of the finite-temperature C-function, defined by Neto and Fradkin [Nucl. Phys. B {\bf 400}, 525 (1993)], is analyzed within a d -dimensional exactly solvable lattice model, recently proposed by Vojta [Phys. Rev. B {\bf 53}, 710 (1996)], which is of the same universality class as the quantum nonlinear O(n) sigma model in the limit $n\to \infty$. The scaling functions of C for the cases d=1 (absence of long-range order), d=2 (existence of a quantum critical point), d=4 (existence of a line of finite temperature critical points that ends up with a quantum critical point) are derived and analyzed. The locations of regions where C is monotonically increasing (which depend significantly on d) are exactly determined. The results are interpreted within the finite-size scaling theory that has to be modified for d=4. PACS number(s): 05.20.-y, 05.50.+q, 75.10.Hk, 75.10.Jm, 63.70.+h, 05.30-d, 02.30