DEPARTMENT OF PHYSICS DISSERTATION: Akshat Pandey

Ph.D. Candidate:  Akshat Pandey

Research Advisor:  Steve Kivelson

Date:  Friday, May 16, 2025 

Time:  10:00 am PST

Location:  McCullough 335

Zoom link: https://stanford.zoom.us/j/98176597554

Email physicsstudentservices [at] stanford.edu (physicsstudentservices[at]stanford[dot]edu) for password. 

Title:  Infinite randomness at the ferromagnet to spin glass transition in the 2d Ising model  

Abstract:  The classical two-dimensional Ising model with random bonds of both signs undergoes a ferromagnet-to-paramagnet transition at low temperatures which is still poorly understood. This transition is governed by a zero-temperature fixed point that separates ferromagnet and spin glass phases. Leveraging the mapping of the model’s ground states to the minimal-weight perfect matching problem, we numerically study the critical properties of large systems. At low temperatures, we establish a connection between the spectrum of the matrix whose Pfaffian determines the Ising partition function, and the energy of optimized defects in the matching problem. We demonstrate that this spectrum exhibits an infinite-randomness singularity at the transition, with a tunneling exponent equal to the stiffness exponent at criticality. We comment on relations to dimerization-driven transitions in random dimer models, and to finite-temperature spin glass phases in higher dimensions.