Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Violation of the Arrhenius law below the transition temperature   When interacting spin systems possess non-zero magnetization or topological
entanglement entropy below the transition temperature, they often serve as
classical or quantum self-correcting memory. In particular, their memory time
grows exponentially in the system size due to polynomially growing energy
barrier, as in the 2D Ising model and 4D Toric code. Here, we argue that this
is not always the case. We demonstrate that memory time of classical clock
model (a generalization of ferromagnet to q-state spins) may be polynomially
long even when the system possesses finite magnetization. This weak violation
of the Arrhenius law occurs above the percolation temperature, but below the
transition temperature, a regime where excitation droplets percolate the entire
lattice, yet the system retains a finite magnetization. We present numerical
evidences for polynomial scaling as well as analytical argument showing that
energy barrier is effectively suppressed and is only logarithmically divergent.
We also suggest an intriguing possibility of experimentally observing the
precession of magnetization vectors at experimentally relevant time scale.

1
The categories of this paper are: cs
10
The categories of this paper are: q-bio
12
The categories of this paper are: nucl-th
2
The categories of this paper are: math
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
24
The categories of this paper are: dg-ga
16
The categories of this paper are: stat
11
The categories of this paper are: hep-lat
15
The categories of this paper are: nucl-ex
17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph