Critical exponents from cluster coefficients

Accurate critical exponents from the -expansion

Critical exponents from general distributions of zeroes

All of the thermodynamic information on a statistical mechanical system is encoded in the locus and density of its partition function zeroes. Recently, a new technique was developed which enables the extraction of the latter using finite-size data of the type typically garnered from a computational approach. Here that method is extended to deal with more general cases. Other critical points of ...

Critical exponents from optimised renormalisation group flows

Within the exact renormalisation group, the scaling solutions for O(N) symmetric scalar field theories are studied to leading order in the derivative expansion. The Gaussian fixed point is examined for d > 2 dimensions and arbitrary infrared regularisation. The Wilson-Fisher fixed point in d = 3 is studied using an optimised flow. We compute critical exponents and subleading corrections-to-scal...

Critical Exponents from Non-Linear Functional Equations for Partially Directed Cluster Models

We present a method for the derivation of the generating function and computation of critical exponents for several cluster models (staircase, bar-graph, and directed columnconvex polygons, as well as partially directed self-avoiding walks), starting with nonlinear functional equations for the generating function. By linearising these equations, we first give a derivation of the generating func...

Critical Exponents from the Effective Average Action

We compute the critical behaviour of three-dimensional scalar theories using a new exact non-perturbative evolution equation. Our values for the critical exponents agree well with previous precision estimates.