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This paper introduces a tensor network (TN) approach for computing partition functions of interacting particle systems in continuous space, traditionally limited to lattice models. They achieve this by discretizing real space and employing a cell-based coarse-graining scheme to create an effective lattice model that preserves spatial locality. Applied to the 2D hard-disk problem, the TN method demonstrates superior performance compared to Monte Carlo simulations.
Tensor networks, previously confined to lattice models, can now efficiently tackle continuous-space statistical mechanics problems, outperforming Monte Carlo in hard-disk simulations.
Tensor network (TN) methods are well established for computing partition functions in statistical mechanics, though this use has traditionally been limited to lattice models. We extend the scope of TN methodology to interacting particle systems in continuous space. Through a real-space discretization combined with a cell-based coarse-graining scheme, we formulate an effective lattice model that explicitly preserves spatial locality. The partition function of this model is represented as a TN, and the thermodynamic quantities are computed via boundary contraction. We apply this framework to the two-dimensional hard-disk problem and demonstrate the strengths of the TN formulation compared to existing Monte Carlo simulations.
