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2014

Relations between Short Range and Long Range Ising models

Angelini, Maria Chiara, Parisi, Giorgio, Ricci-Tersenghi, Federico

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We perform a numerical study of the long range (LR) ferromagnetic Ising model with power law decaying interactions ($J \propto r^{-d-\sigma}$) both on a one-dimensional chain ($d=1$) and on a square lattice ($d=2$).

We use advanced cluster algorithms to avoid the critical slowing down.
We first check the validity of the relation connecting the critical behavior of the LR model with parameters $(d,\sigma)$ to that of a short range (SR) model in an equivalent dimension $D$.
We then study the critical behavior of the $d=2$ LR model close to the lower critical $\sigma$, uncovering that the spatial correlation function decays with two different power laws: the effect of the subdominant power law is much stronger than finite size effects and actually makes the estimate of critical exponents very subtle.

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