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On the mean-field equations for ferromagnetic spin systems

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Abstract

We derive mean-field equations for a general class of ferromagnetic spin systems with an explicit error bound in finite volumes. The proof is based on a link between the mean-field equation and the free convolution formalism of random matrix theory, which we exploit in terms of a dynamical method. We present three sample applications of our results to Kać interactions, randomly diluted models, and models with an asymptotically vanishing external field.

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Acknowledgements

We thank M. Biskup, G. Genovese and S. Warzel for their helpful comments.

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  1. Department of Mathematics, Harvard University, Cambridge, MA, USA

    Christian Brennecke & Per von Soosten

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  1. Christian Brennecke
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  2. Per von Soosten
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Correspondence to Per von Soosten.

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The work of P.S. is supported by the DFG grant SO 1724/1-1.

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Brennecke, C., Soosten, P.v. On the mean-field equations for ferromagnetic spin systems. Lett Math Phys 111, 108 (2021). https://doi.org/10.1007/s11005-021-01450-w

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  • DOI: https://doi.org/10.1007/s11005-021-01450-w

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