Related papers: 3D-Ising Model as a String Theory in Three Dimenti…
String breaking is a central dynamical process in theories featuring confinement, where a string connecting two charges decays at the expense of the creation of new particle-antiparticle pairs. Here, we show that this process can also be…
The critical properties of the 2D Ising and 3-state Potts models are investigated using Monte Carlo simulations. Special interest is given to measurement of 3-point correlation functions and associated universal objects, i.e. structure…
We consider the influence of a power-law deviation from the critical coupling such that the system is critical at its surface. We develop a scaling theory showing that such a perturbation introduces a new length scale which governs the…
We construct a weight matrix for the 3D Ising model satisfying the so-called twisted tetrahedron equation. The result is based on the theory of the n-simplicial complex and the invented recursion procedure on the space of n-simplex…
In the Yang-Mills theory, the apparent thickness of the confining string is known to grow logarithmically when its length increases. The same logarithmic broadening also happens to strings in other quantum field theories and domain walls in…
All-order strong coupling simulations have been used to derive precise energies of string states in the confined phase of three dimensional Z(2) lattice gauge theory. The behavior of the ground state energy is here compared with predictions…
We show that current estimates of the critical exponents of the three-dimensional random-field Ising model are in agreement with the exponents of the pure Ising system in dimension 3 - theta where theta is the exponent that governs the…
In this work, the computational complexity of a spin-glass three-dimensional (3D) Ising model (for the lattice size N = lmn, where l, m, n are the numbers of lattice points along three crystallographic directions) is studied. We prove that…
A powerful existing technique for evaluating statistical mechanical quantities in two-dimensional Ising models is based on constructing a matrix representing the nearest neighbor spin couplings and then evaluating the Pfaffian of the…
We present a random-interface representation of the three-dimensional (3D) Ising model based on thermal fluctuations of a uniquely defined geometric spin cluster in the 3D model and its 2D cross section. Extensive simulations have been…
Three-dimensional spin models of the Ising and XY universality classes are studied by a combination of high-temperature expansions and Monte Carlo simulations. Critical exponents are determined to very high precision. Scaling amplitude…
In this work, we study and evaluate the impact of a periodic spin-lattice coupling in an Ising-like system on a 2D triangular lattice. Our proposed simple Hamiltonian considers this additional interaction as an effect of preferential phonon…
In critical lattice models, distance ($r$) dependent correlation functions contain power laws $r^{-2\Delta}$ governed by scaling dimensions $\Delta$ of an underlying continuum field theory. In Monte Carlo simulations, the leading dimensions…
A classification of discrete integrable systems on quad-graphs, i.e. on surface cell decompositions with quadrilateral faces, is given. The notion of integrability laid in the basis of the classification is the three-dimensional…
The class of random-cluster models is a unification of a variety of stochastic processes of significance for probability and statistical physics, including percolation, Ising, and Potts models; in addition, their study has impact on the…
We study the tricritical Ising universality class using conformal bootstrap techniques. By studying bootstrap constraints originating from multiple correlators on the CFT data of multiple OPEs, we are able to determine the scaling dimension…
The method of counting loops for calculating the partition function of the Ising model on the two dimensional square lattice is extended to lacunary planar lattices, especially scale invariant fractal lattices, the Sierpi\'nsky carpets with…
Recently, it has been shown that, when the dimension of a graph turns out to be infinite dimensional in a broad sense, the upper critical surface and the corresponding critical behavior of an arbitrary Ising spin glass model defined over…
We explain how fractional spin and statistics are relevant to (super)strings in a three-dimensional (3D) Minkowski spacetime.
Classical multidimensional scaling is a widely used method in dimensionality reduction and manifold learning. The method takes in a dissimilarity matrix and outputs a low-dimensional configuration matrix based on a spectral decomposition.…