O(N) Vector Models in the Limit $g \rightarrow g_c $ and Finite Temperature

TL;DR

This paper explores the behavior of O(N) vector models in the large N limit near critical coupling, revealing insights into their structure and phase transitions at finite temperature, with implications for quantum field theory descriptions.

Contribution

It introduces a specific limiting procedure for O(N) models at critical coupling and analyzes the effects of finite temperature on vacuum stability.

Findings

A special limiting procedure is necessary to properly define the theory at critical coupling.

Finite temperature causes the disappearance of a metastable false vacuum.

Insights into the connection between vector models and extended objects in quantum field theory.

Abstract

In the limit where $N\to\infty$ and the coupling constant $g \to g_{c}$ in a correlated manner, O(N) symmetric vector models represent filamentary surfaces. The purpose of these studies is to gain intuition for the long lasting search for a possible description of quantum field theory in terms of extended objects. It is shown here that a certain limiting procedure has to be followed in order to avoid several difficulties in establishing the theory at a critical negative coupling constant. It is also argued that at finite temperature a certain metastable-false vacuum disappears as the temperature is increased.