Exploring Phase Transitions in One-Dimensional Diluted Power-Law XY Spin Glass: A Numerical Investigation

For decades, the behavior of finite-dimensional spin glasses at low temperatures has been a subject of ongoing debate. The physics of spin glasses has been described using two primary frameworks: the replica symmetry breaking (RSB) picture and the droplet picture. In this poster presentation, we focus on our recent work investigating the AT line in the 1D power-law diluted XY spin glass model. Initially, we describe the MCMC methods employed, including a specialized heatbath algorithm tailored for XY spins, showcasing its novelty. Our study reveals clear evidence of an AT line for σ=0.6 in the mean-field regime. For σ=0.75, finite-size scaling studies support the presence of an AT transition, but for σ=0.85, there is no evidence of a transition. Furthermore, we investigated these systems at a fixed temperature while varying the field and discovered that at both σ=0.75 and at σ=0.85, there is evidence of an AT transition! Additionally, we studied a new quantity R and its scaling with system size N for different values of σ. We observe an increasing trend in R with increasing N for σ values greater than 2/3, while for σ=0.6, R decreases with N. This shift in the trend of R with N results from the absence of a phase transition for σ>2/3 in the presence of a magnetic field. Combining our simulation results, we argue that even a slight amount of external magnetic field leads to the destruction of the spin glass phase in short-range models, aligning our findings more with the droplet picture than the RSB picture.