High-precise determination of critical exponents in holographic QCD

Abstract

The precise determination of critical exponents is crucial for understanding the properties of strongly interacting matter under extreme conditions. These exponents are fundamentally linked to the system's behavior near the critical end point (CEP), making precise localization of the CEP essential. However, precisely identifying the CEP within the framework of AdS/CFT correspondence presents considerable challenges. In this study, we explore critical phenomena and critical exponents within a holographic QCD model. We achieve high-precision calculations of the CEP's position and dynamically analyze the behavior of the critical exponent as it approaches the CEP using limiting methods. Our results indicate that linear fitting is only appropriate in regions very close to the CEP. Furthermore, we find that although the values of the critical exponents vary when approaching the CEP from different directions, they ultimately converge to a single fixed value, revealing a universal behavior among these exponents. Our research underscores the importance of precisely determining the CEP, selecting the fitting region, and considering the direction of the approach when predicting critical exponents. These findings establish a vital benchmark for identifying critical phenomena and their associated exponents.