Fluctuation dominated phase ordering in coarse-grained depth models: Domain wall structures, extreme values and coarsening

TL;DR

This paper investigates fluctuation dominated phase ordering in coarse-grained depth models, analyzing domain wall structures, extreme values, and coarsening dynamics through analytical and numerical methods, revealing unique scaling behaviors and phase transition characteristics.

Contribution

It introduces a detailed analysis of FDPO in CD models, including new insights into domain wall fluctuations, coarsening laws, and a mapping to the TIDSI model with a mixed order transition.

Findings

Domain wall number fluctuations are strong but variance remains constant during coarsening.

Largest domain size grows with a power law involving logarithmic corrections.

The generalized model exhibits a mixed order phase transition.

Abstract

Models of particles driven by a one-dimensional fluctuating surface are known to exhibit fluctuation dominated phase ordering (FDPO), in which both the order and fluctuations appear on macroscopic scales. Highly dynamic and macroscopically broad interfacial regions, each composed of many domain walls, appear between macroscopically ordered regions and consequently the scaled correlation function violates the Porod law. We focus on two essential quantities which together quantify the unique characteristics of FDPO, namely the total number of domain walls and the length of the largest ordered domain. We present results in the context of coarse-grained depth (CD) models, both in steady state and while coarsening. Analytic arguments supported by numerical simulations show that even though domain wall number fluctuations are very strong, the associated variance remains constant in time during coarsening. Further, the length of the largest cluster grows as a power law with multiplicative logarithms which involve both the time and system size. In addition, we identify corrections to the leading power law scaling in several quantities in the coarsening regime. We also study a generalisation of the CD model in which the domain wall density is controlled by a fugacity and show that it maps on to the truncated inverse distance squared Ising (TIDSI) model. The generalised model shows a mixed order phase transition, with the regular CD model (which exhibits FDPO) corresponding to the critical point.