There are No Nice Interfaces in 2+1 Dimensional SOS-Models in Random Media

We discuss the underlying connections among the thermodynamic properties of short-ranged spin glasses, their behavior in large finite volumes, and the interfaces that separate different pure states, and also ground states and low-lying excitations.

We study the pinning phase transition for discrete surface dynamics in random environments. A renormalization procedure is devised to prove that the interface moves with positive velocity under a finite size condition. This condition is then checked for different examples of microscopic dynamics to illustrate the flexibility of the method. We show in our examples the existence of a phase transition for various models, including high dimensional interfaces, dependent environme...

This paper has been withdrawn by the authors due to an error in the main theorem.

We review recent results as well as ongoing work and open problems concerning interface states in quantum spin systems at zero and finite temperature.

We present a unified approach to thermodynamic description of one, two and three dimensional phases and phase transformations among them. The approach is based on a rigorous definition of a phase applicable to thermodynamic systems of any dimensionality. Within this approach, the same thermodynamic formalism can be applied for the description of phase transformations in bulk systems, interfaces, and line defects separating interface phases. For both lines and interfaces, we r...

We show that the theoretical machinery developed for the Kardar-Parisi-Zhang (KPZ) class in low dimensions are obeyed by the restricted solid-on-solid (RSOS) model for substrates with dimensions up to $d=6$. Analyzing different restriction conditions, we show that height distributions of the interface are universal for all investigated dimensions. It means that fluctuations are not negligible and, consequently, the system is still below the upper critical dimension at $d=6$. ...

We study equilibrium droplets in two-phase systems at parameter values corresponding to phase coexistence. Specifically, we give a self-contained microscopic derivation of the Gibbs-Thomson formula for the deviation of the pressure and the density away from their equilibrium values which, according to the interpretation of the classical thermodynamics, appears due to the presence of a curved interface. The general--albeit heuristic--reasoning is corroborated by a rigorous pro...

Interface free energy is the contribution to the free energy of a system due to the presence of an interface separating two coexisting phases at equilibrium. It is also called surface tension. The content of the paper is 1) the definition of the interface free energy from first principles of statistical mechanics; 2) a detailed exposition of its basic properties. We consider lattice models with short range interactions, like the Ising model. A nice feature of lattice models i...

The low-temperature driven or thermally activated motion of several condensed matter systems is often modeled by the dynamics of interfaces (co-dimension-1 elastic manifolds) subject to a random potential. Two characteristic quantitative features of the energy landscape of such a many-degree-of-freedom system are the ground-state energy and the magnitude of the energy barriers between given configurations. While the numerical determination of the former can be accomplished in...

We consider various random models (directed polymer, random ferromagnets, spin-glasses) in their disorder-dominated phases, where the free-energy cost $F(L)$ of an excitation of length $L$ presents fluctuations that grow as a power-law $\Delta F(L) \sim L^{\theta}$ with the 'droplet' exponent $\theta$. Within the droplet theory, the energy and entropy of such excitations present fluctuations that grow as $\Delta E(L) \sim \Delta S(L) \sim L^{d_s/2}$ where $d_s$ is the dimensi...