Critical exponents for higher order phase transitions: Landau theory and RG flow

Abstract

In this work, we define and calculate critical exponents associated with higher order thermodynamic phase transitions. Such phase transitions can be classified into two classes: with or without a local order parameter. For phase transitions involving a local order parameter, we write down the Landau theory and calculate critical exponents using the saddle point approximation. Further, we investigate fluctuations about the saddle point and demarcate when such fluctuations dominate over saddle point calculations by introducing the generalized Ginzburg criteria. We use Wilsonian RG to derive scaling forms for observables near criticality and obtain scaling relations between the critical exponents. Afterwards, we find out fixed points of the RG flow using the one-loop beta function and calculate critical exponents about the fixed points for third and fourth order phase transitions.

arXiv commentRevised version of the draft accepted by Journal of Statistical Mechanics for publication

References in corpus (18)

• Large $N$ Phase Transition in Continuum QCD${}_2$
• Top eigenvalue of a random matrix: large deviations and third order phase transition
• Non-intersecting Brownian walkers and Yang-Mills theory on the sphere
• Phase Transitions in the Distribution of Bipartite Entanglement of a Random Pure State
• Distributions of Conductance and Shot Noise and Associated Phase Transitions
• Phase transitions of bipartite entanglement
• Critical Behaviour of the Number of Minima of a Random Landscape at the Glass Transition Point and the Tracy-Widom distribution
• Living at the Edge: A Large Deviations Approach to the Outage MIMO Capacity
• Exact extremal statistics in the classical $1d$ Coulomb gas
• Phase transitions and metastability in the distribution of the bipartite entanglement of a large quantum system
• Third-order phase transition in random tilings
• Universality of the third-order phase transition in the constrained Coulomb gas
• Phase transitions in the distribution of the Andreev conductance of superconductor-metal junctions with multiple transverse modes
• Thermodynamics of the Superconducting Phase Transition in Ba_{0.6}K_{0.4}BiO_3
• Properties of Higher-Order Phase Transitions
• Theory of a Higher Order Phase Transition: Superconducting Transition in BKBO
• Spatial Structures in a Generalized Ginzburg-Landau Free Energy
• Properties of Phase transitions of a Higher Order

Cited by in corpus (1)

• Dynamical quantum phase transitions from random matrix theory