On Spin and Matrix Models in the Complex Plane

Abstract

We describe various aspects of statistical mechanics defined in the complex temperature or coupling-constant plane. Using exactly solvable models, we analyse such aspects as renormalization group flows in the complex plane, the distribution of partition function zeros, and the question of new coupling-constant symmetries of complex-plane spin models. The double-scaling form of matrix models is shown to be exactly equivalent to finite-size scaling of 2-dimensional spin systems. This is used to show that the string susceptibility exponents derived from matrix models can be obtained numerically with very high accuracy from the scaling of finite-$N$ partition function zeros in the complex plane.

25 pages with 5 postscript figures included. LaTeX file with style file crnart11.sty included. CERN--TH-6956/93, FSU-SCRI-93-87

References in corpus (5)

• Renormalization Group Approach to Matrix Models
• Renormalization Group Analysis of Finite-Size Scaling in the ${\Phi }_4^4$ Model
• $O(N)$ Vector Field Theories in the Double Scaling Limit
• The D=1 Matrix Model and the Renormalization Group
• Non-analyticity in the large N renormalization group

Cited by in corpus (16)

• Dynamical quantum phase transitions: scaling and universality
• Multicritical Microscopic Spectral Correlators of Hermitian and Complex Matrices
• Complex-Temperature Phase Diagrams for the q-State Potts Model on Self-Dual Families of Graphs and the Nature of the $q\to \infty$ Limit
• Density of Partition Function Zeroes and Phase Transition Strength
• Large-N phase transition in lattice 2-d principal chiral models
• Uniformizing Lee-Yang Singularities
• Complex RG flows for 2D nonlinear O(N) sigma models
• Lines of Fisher's zeros as separatrices for complex renormalization group flows
• Singularites at a Dense Set of Temperature in Husimi Tree
• Non-Perturbative Large N Trans-series for the Gross-Witten-Wadia Beta Function
• Critical Behavior of Simplicial Chiral Models
• The zeros of the QCD partition function
• Introductory Lectures on Resurgence: CERN Summer School 2024
• A Remark on the Renormalization Group Equation for the Penner Model
• Fisher's zeros as boundary of RG flows in complex coupling space
• Fisher's zeros, complex RG flows and confinement in LGT models