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title: "Aperiodic Interactions on Hierarchical Lattices: an Exact Criterion for the Potts Ferromagnet Criticality • CBPF Index"
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**Physics Note****Published**

# **Aperiodic Interactions on Hierarchical Lattices: an Exact Criterion for the Potts Ferromagnet Criticality**

**A. C. N. Magalhães; S.R. Salinas; C. Tsallis**

1998

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## **Publication details**

<dl>

<dt>Authors</dt>
<dd>A. C. N. Magalhães; S.R. Salinas; C. Tsallis</dd>

<dt>Type</dt>
<dd>Physics Note</dd>

<dt>Status</dt>
<dd>Published</dd>

<dt>Publication date</dt>
<dd>1998</dd>

<dt>Description</dt>
<dd>We discuss the critical behavior of the q-state Potts model on any diamond-like hierarchical lattice with ferromagnetic interactions according to an arbitrary aperiodic two-letter substitutional sequence. We show that the geometric (deterministic) fluctuations become relevant for &lt;math&gt;\omega &gt;1-D/(2-\alpha _u)\,\!&lt;/math&gt; , where &lt;math&gt; \omega\,\!&lt;/math&gt; is the wandering exponent of the substitutional sequence, D is the fractal dimension of the lattice, and &lt;math&gt;\alpha _u\,\!&lt;/math&gt; is the critical exponent associated with the specific heat of the uniform model. Also, we point out that the criteria for analysing the relevance of deterministic and random fluctuations are generically ''different''.</dd>

<dt>Year</dt>
<dd>1998</dd>

<dt>Number</dt>
<dd>CBPF-NF-009/98</dd>

<dt>Linked to a thesis</dt>
<dd>No</dd>

<dt>Linked to a grant</dt>
<dd>No</dd>

</dl>

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