Abstract
Upper bounds are obtained for spin ±1 systems. In the case of only nearestneighbor interactions on, for example, the square lattice we obtainΒ cJ>0.3592. The method's strength is seen when considering systems with longer-range interactions. For example, we obtainΒ cJ>0.360 compared to the previous best bound ofΒ c J⩾ 0.345 for the one-dimensional lattice with 1/r 2 interactions. The method relies upon an identity between correlation functions and then the use of correlation inequalities to obtain the final bounds.
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Monroe, J.L. Upper bounds on the critical temperature for various ising models. J Stat Phys 40, 249–257 (1985). https://doi.org/10.1007/BF01010536
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DOI: https://doi.org/10.1007/BF01010536