A refinement of Simon's correlation inequality |
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Authors: | Elliott H Lieb |
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Institution: | (1) Departments of Mathematics and Physics, Princeton University, 08544 Princeton, NJ, USA |
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Abstract: | A general formulation is given of Simon's Ising model inequality:
whereB is any set of spins separating from . We show that ![lang](/content/xp01307145q38jk2/xxlarge9001.gif)
b
can be replaced by ![lang](/content/xp01307145q38jk2/xxlarge9001.gif)
b
A
whereA is the spin system inside B containing . An advantage of this is that a finite algorithm can be given to compute the transition temperature to any desired accuracy. The analogous inequality for plane rotors is shown to hold if a certain conjecture can be proved. This conjecture is indeed verified in the simplest case, and leads to an upper bound on the critical temperature. (The conjecture has been proved in general by Rivasseau. See notes added in proof.)Work partially supported by U.S. National Science Foundation grant PHY-7825390 A01 |
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Keywords: | |
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