相关论文: New Universality Classes in One--Dimensional $O(N)…

An interplay between non-Hermiticity and disorder plays an important role in condensed matter physics. Here, we report the universal critical behaviors of the Anderson transitions driven by non-Hermitian disorders for three dimensional (3D)…

We consider uniform random permutations in proper substitution-closed classes and study their limiting behavior in the sense of permutons. The limit depends on the generating series of the simple permutations in the class. Under a mild…

We show that a wide variety of generalized increasing subsequence problems admit a one parameter family of extensions for which we can exactly compute the mean length of the longest increasing subsequence. By the nature of the extension,…

We give a new formula for the Chern-Schwartz-MacPherson class of a hypersurface in a nonsigular compact complex analytic variety. In particular this formula generalizes our previous result on the Euler characteristic of such a hypersurface.…

We consider systems whose steady-states exhibit a nonequilibrium phase transition from an active state to one -among an infinite number- absorbing state, as some control parameter is varied across a threshold value. The pair contact…

A new approach to the problem of finding the asymptotical behaviour of large orders of semiclassical expansion is suggested. Asymptotics of high orders not only for eigenvalues, but also for eigenfunctions, are constructed. Thus, one can…

The O$(N)$ vector model in the presence of a boundary has a non-trivial fixed point in $(4-\epsilon)$ dimensions and exhibits critical behaviors described by boundary conformal field theory. The spectrum of boundary operators is…

We consider (random) walks in a multidimensional orthant. Using the idea of universality in probability theory, one can associate a unique polyhedral domain to any given walk model. We use this connection to prove two sets of new results.…

The critical behaviour of the O(n)-symmetric model with two n-vector fields is studied within the field-theoretical renormalization group approach in a D=4-2 epsilon expansion. Depending on the coupling constants the beta-functions, fixed…

The multicritical points of the $O(N)$ invariant $N$ vector model in the large $N$ limit are reexamined. Of particular interest are the subtleties involved in the stability of the phase structure at critical dimensions. In the limit $N \to…

Critical transitions are observed in many complex systems. This includes the onset of synchronization in a network of coupled oscillators or the emergence an epidemic state within a population. "Explosive" first-order transitions have…

We analyze scaling functions in the $3$-$d$, $Z(2)$, $O(2)$ and $O(4)$ universality classes and their finite size dependence using Monte Carlo simulations of improved $\phi^4$ models. Results for the scaling functions are fitted to the…

We derive the large-N, all order asymptotic expansion for a system of N particles with mean-field interactions on top of a Coulomb repulsion at temperature 1/\beta, under the assumptions that the interactions are analytic, off-critical, and…

It has been proposed some time ago that the large $N-$limit can be understood as a ``classical limit'', where commutators in some sense approach the corresponding Poisson brackets. We discuss this in the light of some recent numerical…

In this thesis, we explore the critical phenomena in the presence of extended objects, which we call defects, aiming for a better understanding of the properties of non-local objects ubiquitous in our world and a more practical and…

Continuous phase transitions are catalogued into universality classes, families of systems having identical values of all the exponents governing the critical behaviour of their different physical properties. Numerical simulations have been…

We consider $N$ two-dimensional Ising models coupled in presence of quenched disorder and use scale invariant scattering theory to exactly show the presence of a line of renormalization group fixed points for any fixed value of $N$ other…

Statistical properties of parametric motion in ensembles of Hermitian banded random matrices are studied. We analyze the distribution of level velocities and level curvatures as well as their correlation functions in the crossover regime…

The parametric complexity is the key quantity in the minimum description length (MDL) approach to statistical model selection. Rissanen and others have shown that the parametric complexity of a statistical model approaches a simple function…

We investigate a two-dimensional classical $-vector model with a generic nearest-neighbor interaction $W(\bsigma_i\cdot \bsigma_j)$ in the large-N limit, focusing on the finite-temperature transition point at which energy-energy…