ISSN:
1572-9613
Keywords:
Ising model
;
plane rotator model
;
inequalities
;
long-range order
Source:
Springer Online Journal Archives 1860-2000
Topics:
Physics
Notes:
Abstract For a one-dimensional Ising model with interaction energy $$E\left\{ \mu \right\} = - \sum\limits_{1 \leqslant i〈 j \leqslant N} {J(j - i)} \mu _\iota \mu _j \left[ {J(k) \geqslant 0,\mu _\iota = \pm 1} \right]$$ it is proved that there is no long-range order at any temperature when $$S_N = \sum\limits_{k = 1}^N {kJ\left( k \right) = o} \left( {[\log N]^{{1 \mathord{\left/ {\vphantom {1 2}} \right. \kern-\nulldelimiterspace} 2}} } \right)$$ The same result is shown to hold for the corresponding plane rotator model when $$S_N = o\left( {\left[ {{{\log N} \mathord{\left/ {\vphantom {{\log N} {\log \log N}}} \right. \kern-\nulldelimiterspace} {\log \log N}}} \right]} \right)$$
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01022361
