Related papers: The Gaussian free field in interlacing particle sy…
We compute the fluctuations of the magnetization and of the multi-overlaps for the dilute mean field ferromagnet, in the high temperature region. The rescaled magnetization tends to a centered Gaussian variable with variance diverging at…
Correlation functions of the two-dimensional Ising model on the periodic lattice can be expressed in terms of form factors - matrix elements of the spin operator in the basis of common eigenstates of the transfer matrix and translation…
Lattice gauge theories are a powerful language to theoretically describe a variety of strongly correlated systems, including frustrated magnets, high-$T_c$ superconductors, and topological phases. However, in many cases gauge fields couple…
We investigate the mean-field limit for interacting particle systems through a duality-based framework and obtain quantitative estimates on the convergence of marginals as well as on correlation functions. In particular, for merely…
We consider gradient models on the lattice $Z^d$. These models serve as effective models for interfaces and are also known as continuous Ising models. The height of the interface is modelled by a random field with an energy which is a…
We investigate the influence of the vacuum fluctuations of a background electric field over a charged test particle in the presence of a perfectly reflecting flat wall. A switching function connecting different stages of the system is…
Random fields in nature often have, to a good approximation, Gaussian characteristics. We present the mathematical framework for a new and simple method for investigating the non-Gaussian contributions, based on counting the maxima and…
We study the level-set percolation of the Gaussian free field on Z^d, d bigger or equal to 3. We consider a level alpha such that the excursion-set of the Gaussian free field above alpha percolates. We derive large deviation estimates on…
In this paper, we study a random field constructed from the two-dimensional Gaussian free field (GFF) by modifying the variance along the scales in the neighborhood of each point. The construction can be seen as a local martingale transform…
The growing correlation length observed in supercooled liquids as their temperature is lowered has been studied with the aid of a single occupancy cell model. This model becomes more accurate as the density of the system is increased. One…
We present a dual representation of the partition function of the charged scalar field in which the complex action problem at non-zero chemical potential is absent. In this dual representation Monte Carlo simulations are possible and we…
This work is concerned with fractional Gaussian fields, i.e. Gaussian fields whose covariance operator is given by the inverse fractional Laplacian $(-\Delta)^{-s}$ (where, in particular, we include the case $s >1$). We define a lattice…
Fractals are ubiquitous in the natural world, and their connection with phase transitions has been widely observed. This study investigates mechanisms of fractal formation from the perspective of phase transitions. A novel set of…
Gauge potentials with different configurations have been recently realized in the optical lattice experiments. It is remarkable that one of the simplest gauge can generate particle energy spectrum with the self-similar structure known as a…
We relate the Gaussian free field on a planar domain to the variational formula of Hadamard which explains the change of the Green function under a perturbation of the domain. This is accomplished by means of a natural integral operator…
On the basis of a nonperturbative scalar model of gluon condensate the model of glueball is considered. Two scalar fields describe quantum fluctuations of gauge potential components belonging to a small subgroup $SU(2) \subset SU(3)$ and a…
Intrinsic fluctuations around the solution of the lattice Boltzmann equation are described or modeled by addition of a white Gaussian noise source. For stationary states a fluctuation-dissipation theorem relates the variance of the…
The dynamics of a particle interacting with random classical field in a two-well potential is studied by the functional integration method. The probability of particle localization in either of the wells is studied in detail. Certain…
In the peaks approach, the formation sites of observable structures in the Universe are identified as peaks in the matter density field. The statistical properties of the clustering of peaks are particularly important in this respect. In…
In present work, a relativistic relation that connects the difference of interacting and non-interacting integrated two-particle correlation functions in finite volume to infinite volume scattering phase shift through an integral is…