7 papers
A random walk approach to high-dimensional critical phenomena
Hugo Duminil-Copin, Aman Markar, Romain Panis +1
We present a "black box" proof of mean-field near-critical behaviour for a family of functions on () satisfying a short list of assumptions. The functions repr…
Crossover from subcritical to critical decay: random walk, self-avoiding walk, percolation
Yucheng Liu, Gordon Slade
The study of the Ornstein--Zernike decay of subcritical two-point functions in equilibrium statistical mechanics has a history going back over a century. Despite this, the crossove…
Universal finite-size scaling in high-dimensional critical phenomena
Yucheng Liu, Jiwoon Park, Gordon Slade
We present a new unified theory of critical finite-size scaling for lattice statistical mechanical models with periodic boundary conditions above the upper critical dimension. Our…
Critical scaling profile for trees and connected subgraphs on the complete graph
Yucheng Liu, Gordon Slade
We analyse generating functions for trees and for connected subgraphs on the complete graph, and identify a single scaling profile which applies for both generating functions in a…
The torus plateau for the high-dimensional Ising model
Yucheng Liu, Romain Panis, Gordon Slade
We consider the Ising model on a -dimensional discrete torus of volume , in dimensions and for large , in the vicinity of the infinite-volume critical point …
Near-critical and finite-size scaling for high-dimensional lattice trees and animals
Yucheng Liu, Gordon Slade
We consider spread-out models of lattice trees and lattice animals on , for above the upper critical dimension . We define a correlation length an…