2025/01/11 by Yoshinori Kamijima, Akira Sakai, Kamijima, Yoshinori +1
Physics and Astronomy · #82B10 #82B20 #82B26 #82B27 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Opinion Dynamics and Social Influence #Probability (math.PR) #Statistical Mechanics and Entropy #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2501.06592
openalex publication_date 2025/01/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The transverse-field Ising model is widely studied as one of the simplest quantum spin systems. It is known that this model exhibits a phase transition at the critical inverse temperature βc, which is determined by the spin-spin couplings and the transverse field q ≥ 0. Björnberg [Commun. Math. Phys., 232 (2013)] investigated the divergence rate of the susceptibility for the nearest-neighbor model as the critical point is approached by simultaneously changing the spin-spin coupling J ≥ 0 and q in a proper manner, with fixed temperature. In this paper, we fix J and q and show that the susceptibility diverges as (βc - β)-1 as β\uparrowβc for d>4 assuming an infrared bound on the space-time two-point function. One of the key elements is a stochastic-geometric representation in Björnberg & Grimmett [J. Stat. Phys., 136 (2009)] and Crawford & Ioffe [Commun. Math. Phys., 296 (2010)]. As a byproduct, we derive a new lace expansion for the classical Ising model (i.e., q=0).