We analyse and clarify the finite-size scaling of the weakly-coupled hierarchical $ n $-
component $|\varphi|^ 4$ model for all integers $ n\ge 1$ in all dimensions $ d\ge 4$, for …

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. The universal …

We consider the Ising model on a $ d $-dimensional discrete torus of volume $ r^ d $, in
dimensions $ d> 4$ and for large $ r $, in the vicinity of the infinite-volume critical point …

Two-point functions of random-length random walk on high-dimensional boxes - IOPscience
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The recent discovery of extraordinary-log universality has generated intense interest in
classical and quantum boundary critical phenomena. Despite tremendous efforts, the …

How long does a self-avoiding walk on a discrete d-dimensional torus have to be before it
begins to behave differently from a self-avoiding walk on ℤ d? We consider a version of this …

We obtain precise plateau estimates for the two-point function of the finite-volume weakly-
coupled hierarchical $|\varphi|^ 4$ model in dimensions $ d\ge 4$, for both free and periodic …

We consider spread-out models of lattice trees and lattice animals on $\mathbb Z^ d $, for $
d $ above the upper critical dimension $ d_ {\mathrm c}= 8$. We define a correlation length …

The lattice Green function, ie, the resolvent of the discrete Laplace operator, is fundamental
in probability theory and mathematical physics. We derive its long-distance behaviour via a …

We prove that the scaling limit of the weakly self-avoiding walk on ad-dimensional discrete
torus is Brownian motion on the continuum torus if the length of the rescaled walk is o (V 1∕ …