Related papers: On the two-point function of the Ising model with …
In this paper, we provide the exact expression for the coefficients in the low-temperature series expansion of the partition function of the two-dimensional Ising model on the infinite square lattice. This is equivalent to exact…
In the framework of the 1/N-expansion we show that the Callan-Symanzik beta- function associated with the four-point coupling g is non-analytic at its zero, i.e. at the fixed-point value g^* of g. This behavior can be interpreted by…
The critical behavior of the order-disorder phase transition in the buckled dimer structure of the Si(001) surface is investigated both theoretically by means of first-principles calculations and experimentally by spot profile analysis…
In extensive Monte Carlo simulations the phase transition of the random field Ising model in three dimensions is investigated. The values of the critical exponents are determined via finite size scaling. For a Gaussian distribution of the…
The behavior of two-dimensional Ising spin glasses at the multicritical point on triangular and honeycomb lattices is investigated, with the help of finite-size scaling and conformal-invariance concepts. We use transfer-matrix methods on…
We consider the real $\beta$-ensemble (or 1D log-gas) of dimension $N$ in the high-temperature regime, \textit{i.e.} where the inverse temperature $\beta$ scales as $N\beta=2P$ with $P$ a fixed positive parameter. We establish the large-$N$…
We derive exact analytic results for several four-point correlation functions for statistical models exhibiting phase separation in two-dimensions. Our theoretical results are then specialized to the Ising model on the two-dimensional strip…
The thermal deformation of the critical point action of the 2D tricritical Ising model gives rise to an exact scattering theory with seven massive excitations based on the exceptional $E_7$ Lie algebra. The high and low temperature phases…
In this short note, we establish the following result: Let $f:[0,+\infty[\to [0,+\infty[$, $\alpha:[0,1]\to ]0,+\infty[$ be two continuous functions, with $f(0)=0$. Assume that, for some $a>0$, the function $\xi\to…
In the first part of this work we show the convergence with respect to an asymptotic parameter {\epsilon} of a delayed heat equation. It represents a mathematical extension of works considered previously by the authors [Milisic et al. 2011,…
We study the spin-spin and energy-energy correlation functions for the 2D Ising and 3-states Potts model with random bonds at the critical point. The procedure employed is the renormalisation group approach of the perturbation series around…
The short distance asymptotics of the Ising Model scaling functions are computed for the scaling functions that arise as continuum limits of lattice correlations from below the critical temperature.
An investigation of the performance of the multilevel algorithm in the approach to criticality has been undertaken using the Ising model, performing simulations across a range of temperatures. Numerical results show that the performance of…
We calculate the high-temperature expansion of the 2-point function up to order 800 in beta. We show that estimations of the critical exponent gamma based on asymptotic analysis are not very accurate in presence of confluent logarithmic…
We prove that for $\kappa\in(0,8)$, if $(\eta_1,\eta_2)$ is a $2$-SLE$_\kappa$ pair in a simply connected domain $D$ with an analytic boundary point $z_0$, then $\lim_{r\to 0^+}r^{-\alpha} \mathbb{P}[\mbox{dist}(z_0,\eta_j)<r,j=1,2]$…
The intrinsic 4-point coupling, defined in terms of a truncated 4-point function at zero momentum, provides a well-established measure for the interaction strength of a QFT. We show that this coupling can be computed non-perturbatively and…
We investigate the one-dimensional Ising model with long-range interactions decaying as $1/r^{1+s}$. In the critical regime, for $1/2 \leq s \leq 1$, this system realizes a family of nontrivial one-dimensional conformal field theories…
In this thesis, we present results on phase transition for two models: the semi-infinite Ising model with a decaying field, and the long-range Ising model with a random field. We study the semi-infinite Ising model with an external field…
Recent studies have revealed much of the mathematical structure of the static correlation functions of the XXZ chain. Here we use the results of those studies in order to work out explicit examples of short-distance correlation functions in…
We determine the form factor expansion of the one-point functions in integrable quantum field theory at finite temperature and find that it is simpler than previously conjectured. We show that no singularities are left in the final…