Related papers: The Discrete Gaussian model, II. Infinite-volume s…
We present the results of a finite-size analysis of the four dimensional abelian surface gauge model. This model is defined assigning abelian variables to the plaquettes of an hypercubical lattice, and is dual to the four dimensional Ising…
The free energy and the specific heat of the two-dimensional Gaussian random bond Ising model on a square lattice are found with high accuracy using graph expansion method. At low temperatures the specific heat reveals a zero-temperature…
Boundary constraints in physical, environmental and engineering models restrict smooth states such as temperature to follow known physical laws at the edges of their spatio-temporal domain. Examples include fixed-state or fixed-derivative…
We study the extremal properties of the "integer-valued Gaussian" a.k.a.\ DG-model on the hierarchical lattice $\Lambda_n:=\{1,\dots,b\}^n$ (with $b\ge2$) of depth $n$. This is a random field $\varphi\in\mathbb Z^{\Lambda_n}$ with law…
Plaquette models are short range ferromagnetic spin models that play a key role in the dynamic facilitation approach to the liquid glass transition. In this paper we perform a rigorous study of the thermodynamic properties of two…
An analytic method for deriving the free energy of a three-dimensional Ising-like system near the critical point in a homogeneous external field is developed in the $\rho^6$ model approximation. The mathematical description proposed for…
This paper studies the limits of a spatial random field generated by uniformly scattered random sets, as the density $\lambda$ of the sets grows to infinity and the mean volume $\rho$ of the sets tends to zero. Assuming that the volume…
It has been well known for a long time that the height function of random lozenge tilings of large domains follow a law of large number and possible limits called dimer limit shapes are well understood. For the next order, it is expected…
The residual gas damping of the test mass (TM) in the free molecular flow regime is studied in the finite open systems for high-precision gravity-related experiments. Through strict derivation, we separate the damping coefficients for two…
For a given metric measure space $(X,d,\mu)$ we consider finite samples of points, calculate the matrix of distances between them and then reconstruct the points in some finite-dimensional space using the multidimensional scaling (MDS)…
We consider infinite-dimensional diffusions where the interaction between the coordinates has a finite extent both in space and time. In particular, it is not supposed to be smooth or Markov. The initial state of the system is Gibbs, given…
Based on quasi-stationary distribution ideas, a general finite size scaling theory is proposed for discontinuous nonequilibrium phase transitions into absorbing states. Analogously to the equilibrium case, we show that quantities such as,…
We propose and study a fully implicit finite volume scheme for the pressureless Euler-Poisson-Boltzmann equations on the one dimensional torus. Especially, we design a consistent and dissipative discretization of the force term which yields…
For $d \geq 3$ we obtain an approximation of the zero-average Gaussian free field on the discrete $d$-dimensional torus of large side length $N$ by the Gaussian free field on $\mathbb Z^d$, valid in boxes of roughly side length $N -…
We consider a two-dimensional Bose gas in the dilute regime where $\rho a^2$ is small. For temperatures below the Berezinskii-Kosterlitz-Thouless critical temperature, we derive an explicit upper bound for the free energy density using…
We derive finite-size scaling formulae for four-dimensional Higgs-Yukawa models near the Gaussian fixed point. These formulae will play an essential role in future, detailed investigation of such models. In particular, they can be used to…
We show that $\N=1$ gauge theories with an adjoint chiral multiplet admit a wide class of large-N double-scaling limits where $N$ is taken to infinity in a way coordinated with a tuning of the bare superpotential. The tuning is such that…
We investigate dynamic scaling properties of the two-dimensional gauge glass model for the vortex glass phase in superconductors with quenched disorder. From extensive Monte Carlo simulations we obtain static and dynamic finite size scaling…
We develop a new approach to gravitational waves in which the Einstein equations are governed by the cosmological constant which is related to the existence of a manifold which is closed. We study an example in which the matter Lagrangian…
Global One--Dimensional Quantum General Relativity is the toy model with nontrivial field theoretical content, describing classical one-dimensional massive bosonic fields related to any 3+1 metric, where the dimension is a volume of…