Knauf A (1993)
Publication Type: Journal article, Original article
Publication year: 1993
Publisher: Springer Verlag (Germany)
Book Volume: 73
Pages Range: 423--431
Journal Issue: 1-2
DOI: 10.1007/BF01052771
We present numerical and analytical evidence for a first-order phase transition of the ferromagnetic spin chain with partition function Z(fi) = i(fi \Gamma 1)=i(fi) at the inverse temperature fi cr = 2. KEY WORDS: Riemann zeta function, spin chain, phase transition. In a recent paper [6] we established a link between analytic number theory and classical statistical mechanics by interpreting the quotient Z(s) = i(s \Gamma 1)=i(s) of Riemann zeta functions as the partition function of an infinite spin chain with ferromagnetic interactions. For Re(s) ? 2 the quotient has the Dirichlet series representation Z(s) = 1 X n=1 '(n) \Delta n \Gammas (1) where for n 1 the Euler totient function '(n) is defined to be the number of positive integers not exceeding n which are relatively prime to n (that is, '(n) = #fi 2 f1; : : : ;ng j gcd(i;n) = 1g). Now on any half-plane of the form Re(s) ? 2 + ", " ? 0, Z is uniformly approximated by partition functions...
APA:
Knauf, A. (1993). Phases of the Number-Theoretic Spin Chain. Journal of Statistical Physics, 73(1-2), 423--431. https://dx.doi.org/10.1007/BF01052771
MLA:
Knauf, Andreas. "Phases of the Number-Theoretic Spin Chain." Journal of Statistical Physics 73.1-2 (1993): 423--431.
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