2020/01/06 by James Taylor, Taylor, James H., James Hudson Taylor
Physics and Astronomy · #Complex Network Analysis Techniques #FOS: Physical sciences #Quantum many-body systems #Spectroscopy and Quantum Chemical Studies #Statistical Mechanics (cond-mat.stat-mech) #Theoretical and Computational Physics
paper · pdf · doi:10.48550/arxiv.2001.01693
openalex publication_date 2020/01/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The zero-field isothermal susceptibility of the one-dimensional Ising model\nwith nearest-neighbor interactions and a finite number of spins is shown to\nhave a relatively simple singularity as the temperature approaches zero,\nproportional only to the inverse temperature. This is in contrast to what is\nseen throughout the literature for the inifinite chain: an essential\nsingularity that includes an exponential dependence on the inverse temperature.\nAssuming an arbitrary (but finite) number of spins and retaining terms that are\nusually considered ignorable in the thermodynamic limit, the analysis involves\nnothing beyond straightforward series expansions, starting either from the\npartition function for a closed chain in a magnetic field, obtained using the\ntransfer-matrix approach; or from the expression for the zero-field\nsusceptibility found via the fluctuation-dissipation theorem. In both cases,\nthe exponential singularity is exactly removed. In addition, the susceptibility\nper spin is found to increase with the number of spins (except in the case of\nnoninteracting spins), a result which is also at variance with what is normally\nreported for an infinite chain.\n