Critical behavior at the interface between two systems belonging to different universality classes

Abstract

We consider the critical behavior at an interface which separates two semi-infinite subsystems belonging to different universality classes, thus having different set of critical exponents, but having a common transition temperature. We solve this problem analytically in the frame of φ k meanfield theory, which is then generalized using phenomenological scaling considerations. A large variety of interface critical behavior is obtained which is checked numerically on the example of two-dimensional q-state Potts models with 2 ≤ q ≤ 4. Weak interface couplings are generally irrelevant, resulting in the same critical behavior at the interface as for a free surface. With strong interface couplings, the interface remains ordered at the bulk transition temperature. More interesting is the intermediate situation, the special interface transition, when the critical behavior at the interface involves new critical exponents, which however can be expressed in terms of the bulk and surface exponents of the two subsystems. We discuss also the smooth or discontinuous nature of the order parameter profile.

Numerical study of the critical behavior of the Ashkin–Teller model at a line defect

“…In this case the σ and τ spins play equivalent role and the interface critical behavior has been studied previously in Refs. [11,12]. According to these results, which are in agreement with a relevance-irrelevance analysis [2][3][4][5], the bulk fixed point (B) in the system is unstable for ǫ > 0.…”

“…In contrast for enhanced defect couplings the defect usually renormalizes to an ordered interface and the local critical exponents are the same as at the extraordinary surface transition [6]- [8]. Examples for modified defect critical behavior can be found in the two-dimensional (2D) q = 3-state Potts model [9,10], in the Baxter-Wu model [11] and in the Ashkin-Teller (AT) model [12].…”

Scaling properties at the interface between different critical subsystems: The Ashkin-Teller model

“…This problem has already been addressed in Ref. 5 in which the analytical mean-field solution, in terms of ϕ k field theories, has been obtained and generalized by using phenomenological scaling considerations. Monte Carlo simulations have also been performed in two dimensions for interfaces between subsystems belonging to the universality classes of the Ising model, the three-state and four-state Potts models.…”

“…For some intermediate value of the couplings, there is a special interface transition fixed point, involving new critical exponents, which, however, can be expressed in terms of the bulk and surface exponents of the two subsystems. 5 In the present work our purpose is to examine the different types of possible interface critical behavior which can be realized. Thus, we consider situations where a weak interface coupling can be irrelevant, relevant or even truly marginal.…”

Nonequilibrium critical dynamics of the two-dimensional Ising model quenched from a correlated initial state

“…It is known 37 that nonequilibrium critical dynamics at time t, after a quench at t = 0 from a state with T i = ∞, is analogous to the static critical behavior of a semi-infinite system at a distance y from a free surface located at y = 0. The analogous static critical problem to our dynamical problem here is the interface critical behavior at a distance, y, from a straight interface, which separates two coupled semi-infinite critical systems which belong to different universality classes 39,40 . According to our numerical calculations the nonequilibrium critical behavior in our problem is the result of the interplay and competition between the critical fluctuations of the two systems.…”