# Exploring Structures in Physics Problems: Can AI Agents Discover Statistical Mechanical Mappings?

arXiv: https://arxiv.org/abs/2607.26367 · HTML: https://mlsanity.com/paper/2607.26367/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Web, search, and research agents, one of 16 directions in LLM agents and tool use.
- Builds on 2 of its 32 references that are in the map.
- First posted on arXiv 29 Jul 2026.

## Placed in

- LLM agents and tool use / [Web, search, and research agents](https://mlsanity.com/agents/web-search-and-research-agents/)

## Builds on (most cited first, 2 of 2)

- [An AI system to help scientists write expert-level empirical software](https://mlsanity.com/paper/2509.06503/) (2025)
- [PRL-Bench: A Comprehensive Benchmark Evaluating LLMs' Capabilities in Frontier Physics Research](https://mlsanity.com/paper/2604.15411/) (2026)

## Abstract (arXiv)

An important skill in theoretical physics is to recognize when a new problem can be transformed into a known model. We study this skill as an AI-agent task: can LLM-based agents discover statistical mechanical mappings from a raw partition function to a tractable representation? To probe this question, we introduce StatMechBench-v0, a benchmark of six Ising-type problems covering transfer-matrix methods, gauge-removable disorder, and planar/Pfaffian structure. We evaluate a simple propose-verify-revise agent across multiple LLMs and problem phrasings. The results show that numerical feedback often helps agents repair code and recover correct partition functions. However, agents can also pass the numerical checks while misidentifying the underlying tractable class or understating computational complexity. This both reveals limitations in current LLM reasoning and calls for a verification stack that goes beyond numerical agreement, incorporating, for example, symbolic checks and structural invariants. Our study provides an early evaluation and design directions for AI agents aimed at structural discovery in theoretical physics.