Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Multiple phase transitions on compact symbolic systems   Let $\phi:X\to \mathbb R$ be a continuous potential associated with a
symbolic dynamical system $T:X\to X$ over a finite alphabet. Introducing a
parameter $\beta>0$ (interpreted as the inverse temperature) we study the
regularity of the pressure function $\beta\mapsto P_{\rm top}(\beta\phi)$ on an
interval $[\alpha,\infty)$ with $\alpha>0$. We say that $\phi$ has a phase
transition at $\beta_0$ if the pressure function $P_{\rm top}(\beta\phi)$ is
not differentiable at $\beta_0$. This is equivalent to the condition that the
potential $\beta_0\phi$ has two (ergodic) equilibrium states with distinct
entropies. For any $\alpha>0$ and any increasing sequence of real numbers
$(\beta_n)$ contained in $[\alpha,\infty)$, we construct a potential $\phi$
whose phase transitions in $[\alpha,\infty)$ occur precisely at the
$\beta_n$'s. In particular, we obtain a potential which has a countably
infinite set of phase transitions.

20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph
31
The categories of this paper are: ao-sci
29
The categories of this paper are: funct-an
9
The categories of this paper are: nlin
13
The categories of this paper are: quant-ph
25
The categories of this paper are: patt-sol
6
The categories of this paper are: astro-ph
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ
34
The categories of this paper are: chem-ph
5
The categories of this paper are: gr-qc
3
The categories of this paper are: physics