On Ising model in magnetic field on the lattice

2025/04/25 by Raghav G. Jha, Jha, Raghav G.
Physics and Astronomy · Mathematics · #Theoretical and Computational Physics #Stochastic processes and statistical mechanics #Quantum many-body systems

paper · pdf · doi:10.48550/arxiv.2504.18744

Abstract

We conjecture an approximate expression for the free energy in the thermodynamic limit of the classical square lattice Ising model in a uniform (real) magnetic field. The zero-field result is well known due to Onsager for more than eighty years, but no such result exists for a nonzero magnetic field on a regular lattice. We verify our conjecture using numerical tensor renormalization group (TRG) methods and find good agreement with a maximum deviation of ∼2% from the numerical results for the free energy across all β and real magnetic field, h.

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