Abstract
We obtain new properties of general d-dimensional lattice ferromagnetic spin systems with nearest neighbor interactions in the high-temperature region (β≪1). Each model is characterized by a single-site a priori spin distribution, taken to be even. We state our results in terms of the parameter α=〈s 4〉−3〈s 2〉2, where 〈s k〉 denotes the kth moment of the a priori distribution. Associated with the model is a lattice quantum field theory which is known to contain particles. We show that for α>0, β small, there exists a bound state with mass below the two-particle threshold. The existence of the bound state has implications for the decay of correlations, i.e., the 4-point functions decay at a slower rate than twice that of the 2-point function. These results are obtained using a lattice version of the Bethe–Salpeter equation. The existence results generalize to N-component models with rotationally invariant a priori spin distributions.
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REFERENCES
J. Glimm and A. Jaffe, Quantum Physics, 2nd ed. (Springer, New York, 1986).
R. Schor, Commun. Math. Phys. 59:213–233 (1978).
P. Paes-Leme, Ann. Phys. 115:367–387 (1978).
B. Simon, Statistical Mechanics of Models (Princeton University Press, 1994).
T. Spencer and F. Zirilli, Commun. Math. Phys. 49:1–16 (1976).
J. Dimock and J. P. Eckman, Commun. Math. Phys. 51:41 (1976).
J. Lebowitz, Commun. Math. Phys. 35:87–92 (1974).
R. Ellis, J. Monroe, and C. Newman, Commun. Math. Phys. 46:167–182 (1976).
D. Brydges, J. Frohlich, and T. Spencer, Commun. Math. Phys. 83:123–150 (1983).
R. Schor, J. Barata, P. Veiga, and E. Pereira, Phys. Rev. E. 59(3):2689–2694 (March 1999).
R. Schor and M. O'Carroll, M. Decay of the Bethe-Salpeter kernel for Lattice Classical Ferromagnetic Spin Systems, J. Stat. Phys. 99:1265–1279 (2000).
M. Reed and B. Simon, Modern Methods of Mathematical Physics, Vol. I (Academic Press, New York, 1972).
M. Reed and B. Simon, Modern Methods of Mathematical Physics, Vol. IV (Academic Press, New York, 1978).
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Schor, R.S., O'Carroll, M. Transfer Matrix Spectrum and Bound States for Lattice Classical Ferromagnetic Spin Systems at High Temperature. Journal of Statistical Physics 99, 1207–1223 (2000). https://doi.org/10.1023/A:1018632604807
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DOI: https://doi.org/10.1023/A:1018632604807