相关论文: Critical exponents on Fortuin--Kasteleyn weighted …

We consider random q-state Potts models for $3\le q \le 8$ on the square lattice where the ferromagnetic couplings take two values $J_1>J_2$ with equal probabilities. For any q the model exhibits a continuous phase transition both in the…

Motivated by automated junction recognition in tracking data, we study a problem of placing a square or disc of fixed size in an arrangement of lines or line segments in the plane. We let distances among the intersection points of the lines…

We study corrections to scaling in the O(3)- and O(4)-symmetric phi^4 model on the three-dimensional simple cubic lattice with nearest neighbour interactions. For this purpose, we use Monte Carlo simulations in connection with a finite size…

We show how to use the link representation of the transfer matrix $D_N$ of loop models on the lattice to calculate partition functions, at criticality, of the Fortuin-Kasteleyn model with various boundary conditions and parameter $\beta = 2…

We show how to combine Kesten's scaling relations, the determination of critical exponents associated to the stochastic Loewner evolution process by Lawler, Schramm, and Werner, and Smirnov's proof of Cardy's formula, in order to determine…

This is the first in a series of three papers that addresses the behaviour of the droplet that results, in the percolating phase, from conditioning the Fortuin-Kasteleyn planar random cluster model on the presence of an open dual circuit…

We consider the boundary WZW model on a half-plane with a cut growing according to the Schramm-Loewner stochastic evolution and the boundary fields inserted at the tip of the cut and at infinity. We study necessary and sufficient conditions…

We study the dynamic critical behavior of the Chayes-Machta dynamics for the Fortuin-Kasteleyn random-cluster model, which generalizes the Swendsen-Wang dynamics for the q-state Potts model to noninteger q, in two and three spatial…

We compute the critical exponents for nonextensive $\lambda\phi^{3}$ scalar field theory for all loop orders and $|q - 1| < 1$. We apply the results for both nonextensive percolation and Lee-Yang edge singularity problems. The corresponding…

Many critical properties of the Hintermann-Merlini model are known exactly through the mapping to the eight-vertex model. Wu [J. Phys. C {\bf 8}, 2262 (1975)] calculated the spontaneous magnetizations of the model on two sublattices by…

We consider global 2-SLE$_{\kappa}$ $(\eta_1, \eta_2)$ in a topological rectangle with $\kappa\in (4,8)$. We derive the law of a random hitting point of the curves and show that, conditional on this random hitting point, the pair of two…

The Schramm-Loewner evolution (SLE) is a powerful tool to describe fractal interfaces in 2D critical statistical systems. Yet the application of SLE is well established for statistical systems described by quantum field theories satisfying…

We introduce a renormalized 1PI vertex part scalar field theory setting in momentum space to computing the critical exponents $\nu$ and $\eta$, at least at two-loop order, for a layered parallel plate geometry separated by a distance L,…

We obtain an exact finite-size expression for the probability that a percolation hull will touch the boundary, on a strip of finite width. Our calculation is based on the q-deformed Knizhnik--Zamolodchikov approach, and the results are…

We perform a finite-size scaling analysis of the critical point in the heavy-quark region of QCD at nonzero temperature. Our previous analysis on the Binder cumulant at $N_t=4$ is extended to finer lattices with $N_t=6$ and $8$. The aspect…

We study the phase-ordering of parametrically and incoherently driven microcavity polaritons after an infinitely rapid quench across the critical region. We confirm that the system, despite its driven-dissipative nature, fulfils dynamical…

We apply a variation on the methods of Duminil-Copin, Raoufi, and Tassion to establish a new differential inequality applying to both Bernoulli percolation and the Fortuin-Kasteleyn random cluster model. This differential inequality has a…

The dynamical critical behavior of a single directed line driven in a random medium near the depinning threshold is studied both analytically (by renormalization group) and numerically, in the context of a Flux Line in a Type-II…

For the two-dimensional Q-state Potts model at criticality, we consider Fortuin-Kasteleyn and spin clusters and study the average number N_Gamma of clusters that intersect a given contour Gamma. To leading order, N_Gamma is proportional to…

We study the geometric properties of a system initially in equilibrium at a critical point that is suddenly quenched to another critical point and subsequently evolves towards the new equilibrium state. We focus on the bidimensional Ising…