Numerical Studies of the Random-Field One-Dimensional Long-Range Ising Model

The microscopic mechanisms by which materials change from liquids to solids without the usual crystallization process remains unknown. Whether window glass is a slowly aging liquid, or a true solid remains a longstanding unresolved question in condensed matter physics. Motivated by recent observation of two-dimensional (2D) colloidal glasses, we carried out a Monte Carlo study of the random-field one-dimensional (1D) long-range Ising model. In the pure case, the 1D long-range Ising model has been shown to exhibit the same behavior as the 2D X-Y model with a finite-temperature phase transition. We studied systems of sizes from 50 to 350 spins. The Metropolis algorithm was used for two million steps . We attempted a finite-size scaling (FSS) analysis to calculate the critical temperature and exponents of the system. It was determined that FSS fails in this system due to the likely presence of multiple length scales, so a more nuanced analysis is needed in order to analyze the nature of possible phase transition(s) in this system. This work was supported by NSF-DMR- 2203380.