Abstract

Measurements can be used to probe critical systems, disturb existing criticality, dominate the long-distance behavior, and even generate distinct critical phenomena through the randomness of their outcomes. Within this broad theme, I will talk about two of my recent works that study critical phenomena in the presence of measurements, and where randomness in measurement outcomes plays a key role.

I will first discuss our recent work: https://arxiv.org/abs/2604.06324, where we discover a novel higher Nishimori line in the learning phase diagram of deformed toric codes and classical Ising models under measurements. I will talk about a number of exact results, like the power-law exponent of the Edwards-Anderson correlator at the learning tricritical point in the phase diagram, that follow from this higher Nishimori structure.

Then I will discuss another recent work: https://arxiv.org/abs/2507.07959, where we obtain a non-perturbative theorem that establishes monotonicity of the Casimir effective central charge under RG flows induced by measurements on 2D classical critical points. The existence of this 'c-effective theorem' despite the lack of translational invariance due to random measurement outcomes distinguishes it from previously known monotonicity theorems for RG flows.

More broadly, these results suggest a natural route to classifying measurement-dominated critical phenomena by combining learnability, replica statistical mechanics, and information-theoretic monotonicity.