Related papers: Scaling limits of linear random fields on ${\mathb…
In systems belonging to the universality class of the random field Ising model, the standard hyperscaling relation between critical exponents does not hold, but is replaced by a modified hyperscaling relation. As a result, standard…
Puzzled by the indication of a new critical theory for the spin-1/2 Heisenberg model with a spatially staggered anisotropy on the square lattice as suggested in \cite{Wenzel08}, we re-investigate the phase transition of this model induced…
We evaluate a strongly regularised version of the Hastings-Levitov model HL$(\alpha)$ for $0\leq \alpha<2$. Previous results have concentrated on the small-particle limit where the size of the attaching particle approaches zero in the…
We study scaling laws for singular perturbation problems associated with a class of two-dimensional martensitic phase transformations and deduce a domain dependence of the scaling law in the singular perturbation parameter. In these…
Finite size scaling for a first order phase transition where a continuous symmetry is broken is developed using an approximation of Gaussian probability distributions with a phenomenological "degeneracy" factor included. Predictions are…
We discuss a model for phase transitions in which a double-well potential is singularly perturbed by possibly several terms involving different, arbitrarily high orders of derivation. We study by $\Gamma$-convergence the asymptotic…
A salient feature of cyclically driven first-order phase transformations in crystals is their scale-free avalanche dynamics. This behavior has been linked to the presence of a classical critical point but the mechanism leading to…
Scaling relations are used to study cross-overs, due to anisotropic spin interactions or single ion anisotropy, and due to disorder, in the thermodynamics and correlation functions near quantum-critical transitions. The principal results…
Statistical systems displaying a strongly anisotropic or dynamical scaling behaviour are characterized by an anisotropy exponent theta or a dynamical exponent z. For a given value of theta, we construct local scale transformations which can…
We investigate the evolution of scalar metric perturbations across a sudden cosmological transition, allowing for an inhomogeneous surface stress at the transition leading to a discontinuity in the local expansion rate, such as might be…
The equilibrium amorphous solid state -- formed, e.g., by adequately randomly crosslinking the constituents of a macromolecular fluid -- is a heterogeneous state characterized by a universal distribution of particle localization lengths.…
It has been argued that the small perturbations to the homogeneous and isotropic configurations of a canonical scalar field in an expanding universe do not grow. We show that this is not true in general, and clarify the root of the…
We investigate the finite-size scaling of the boundary quantum geometric tensor (QGT) numerically close to the Anderson localization transition in the presence of small external magnetic fields. The QGT exhibits universal scaling and…
We investigate the cosmic evolution of the linear bias in the framework of a flat FLRW spacetime. We consider metric perturbations in the Newtonian gauge, including Hubble scale effects. Making the following assumptions, (i) scale…
We analyze the critical properties of the three-dimensional Ising model with linear parallel extended defects. Such a form of disorder produces two distinct correlation lengths, a parallel correlation length $\xi_\parallel$ in the direction…
The scaling slope of the anti-symmetric mass gap M of compact U(1)_{2+1} lattice gauge theory is obtained analytically in the Hamiltonian formalism using the plaquette expansion. Based on the first four moments of the Hamiltonian with…
Independent random signs can govern various discrete models that converge to non-isomorphic continuous limits. Convergence of Fourier-Walsh spectra is established under appropriate conditions.
Light scalar fields very naturally appear in modern cosmological models, affecting such parameters of Standard Model as electromagnetic fine structure constant $\alpha$, dimensionless ratios of electron or quark mass to the QCD scale,…
We investigate fluctuation phenomena for the graph distance and the number of cut points associated with random media arising from the range of a random walk. Our results demonstrate a sequence of dimension-dependent phase transitions in…
Consider a linear elliptic partial differential equation in divergence form with a random coefficient field. The solution operator displays fluctuations around its expectation. The recently developed pathwise theory of fluctuations in…