Eigenvalue Degeneracy and Existence and Non‐existence of a Phase Transition in One Dimension | Zendy

Thompson Colin J. | Zendy

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Eigenvalue Degeneracy and Existence and Non‐existence of a Phase Transition in One Dimension

Author(s) -

Thompson Colin J.

Publication year - 1969

Publication title -

studies in applied mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.164

H-Index - 46

eISSN - 1467-9590

pISSN - 0022-2526

DOI - 10.1002/sapm1969484299

Subject(s) - eigenvalues and eigenvectors , mathematics , degeneracy (biology) , phase transition , dimension (graph theory) , ising model , perturbation (astronomy) , mathematical physics , order (exchange) , combinatorics , physics , statistical physics , condensed matter physics , quantum mechanics , biology , bioinformatics , finance , economics

We consider a one dimensional Ising chain with interaction potential J ( k ) such that J ( k ) = 0 when k > n . By a perturbation argument we show that long range order exists at sufficiently low temperatures if and only ifThis is consistent with Dyson's recent theorems and in addition predicts that when J ( k ) = k −2 there is no long range order.

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