Statistical Physics and Thermodynamics Physicist (PhD)

## About the work

CritPt is a public benchmark of research-level physics challenges, built to test whether frontier AI models can carry out genuine physics research reasoning rather than textbook problem solving. The benchmark paper is [arXiv:2509.26574](https://arxiv.org/abs/2509.26574) and we recommend reading it before applying. It will tell you quickly whether this work interests you.

We are engaging physicists to work on research-level physics problems in their own subfield. Depending on where your publication record fits, that can mean creating problems, solving them, reviewing completed work, or auditing it. We agree the specific assignment with you once you are matched to an area.

This is research-grade work rather than volume work. Whatever you produce has to be complete enough for another specialist in your subfield to follow and verify independently, so written reasoning is part of every assignment.

## Research areas in this panel

Five areas. We match narrowly: you need to have published on one of these specific phenomena, not in statistical physics broadly. Each area lists the methods it requires.

1. Disordered spin models and the Nishimori line, QEC thresholds, mixed-state topological order: Replicated random-bond Ising model, Nishimori line and gauge symmetry of disordered spin models, quenched disorder averaging, Kramers-Wannier duality and square-lattice self-duality, Ashkin-Teller coupled Ising flavors, domain-wall free energy from twisted boundary conditions, exact lattice evaluation of Ising partition functions, decoherence-induced mixed-state topological order and quantum memory thresholds.

2. Entanglement entropy via the replica trick, Goldstone modes and tower of states: Replica trick, analytic continuation in the replica index, Gaussian lattice sums and theta functions, Poisson summation and modular transformations, Renyi and von Neumann entanglement entropies, Goldstone modes and tower-of-states structure.

3. Range expansions with long-range dispersal, front propagation, heavy-tailed jumps: Long-range dispersal kernels, heavy-tailed jump processes, stratified diffusion and coalescing colony models, self-consistent mean-field growth equations, convolution integral equations, asymptotic expansions with logarithmic corrections, front propagation in range expansions.

4. Lattice path enumeration and entanglement domain-wall statistical mechanics: Lattice random walks with internal states, generating function methods, first-return decomposition of lattice paths, transfer-matrix partition functions, splitting and recombination of composite excitations, entanglement domain-wall statistical mechanics, weighted path enumeration.

5. Two-dimensional CFT: Ising minimal model, BPZ equations, conformal blocks, Coulomb gas: Two-dimensional conformal field theory, Ising minimal model, Virasoro algebra and degenerate representations, BPZ null-vector differential equations, conformal blocks and crossing symmetry, operator product expansion and fusion rules, Coulomb gas integral representations, free-fermion and bosonization methods.

## Methods we expect to find in your own publications

You should be able to point to your own papers demonstrating at least one of the following families:

• Exact lattice methods: Kramers-Wannier duality, self-duality, transfer-matrix partition functions, exact evaluation of coupled Ising flavors
• Replica and field-theoretic: replica trick and analytic continuation in the replica index, Gaussian lattice sums and theta functions, Renyi and von Neumann entropies
• Asymptotic analysis: convolution integral equations, asymptotic expansions with logarithmic corrections, stratified diffusion, generating function methods
• Conformal: Virasoro algebra, degenerate representations, BPZ null-vector differential equations, operator product expansion and fusion rules, free-fermion and bosonization methods

## Who we are looking for

A PhD in statistical physics, mathematical physics or a closely related field. This is a hard requirement. Postdoctoral researchers, research scientists and junior faculty are the strongest fit. Senior PhD students with a strong first-author record are welcome to apply.

Published work on the specific phenomenon above, not the adjacent one. This is the single most common reason we decline otherwise excellent physicists. Command of the methods is not enough if you have not published on the phenomenon itself.

A verifiable publication record. Three to five representative papers with arXiv IDs or DOIs, ideally from the last five years. First author strongly preferred. Every paper you list will be checked against the public record.

Working proficiency with LaTeX, Python, SymPy and Jupyter. Some familiarity with an agentic coding extension in VS Code is useful. Gaps here are acceptable if you declare them honestly.

English at B2 or above, including written reasoning. A large part of the value you add is how clearly you set out your argument.

## Application steps

1. Apply and complete the attached form. Basic information, education, research experience, your method self-attestation, and up to five of the areas above that you are the best fit for. For each area you select, give an arXiv ID or DOI of your own paper as proof, with your author position and the methods it demonstrates. A selection without proof is not scored.

2. We verify your papers and authorship against the public record.

3. Then one of two things happens. Either we onboard you directly, or we invite you to a short live alignment call to agree the area and the assignment with you.

4. A brief 30 to 45 minute assessment may be added, but only where we need it. Most applicants will not see one.

## Commitment and rate

10 hours per week, sustained across an 8 to 10 week window, starting immediately. Remote and asynchronous with no fixed hours.

$80 to $110 per hour, set by depth of subdomain match.