SciPost Phys. 10, 113 (2021) ·
published 26 May 2021
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We develop further the study of a system in contact with a multibath having
different temperatures at widely separated timescales. We consider those
systems that do not thermalize in finite times when in contact with an ordinary
bath but may do so in contact with a multibath. Thermodynamic integration is
possible, thus allowing one to recover the stationary distribution on the basis
of measurements performed in a `multi-reversible' transformation. We show that
following such a protocol the system is at each step described by a
generalization of the Boltzmann-Gibbs distribution, that has been studied in
the past. Guerra's bound interpolation scheme for spin-glasses is closely
related to this: by translating it into a dynamical setting, we show how it may
actually be implemented in practice. The phase diagram plane of temperature vs
"number of replicas", long studied in spin-glasses, in our approach becomes
simply that of the two temperatures the system is in contact with. We suggest
that this representation may be used to directly compare phenomenological and
mean-field inspired models.Finally, we show how an approximate out of
equilibrium probability distribution may be inferred experimentally on the
basis of measurements along an almost reversible transformation.
Federico Corberi, Alessandro Iannone, Manoj Kumar, Eugenio Lippiello, Paolo Politi
SciPost Phys. 10, 109 (2021) ·
published 18 May 2021
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We study the kinetics after a low temperature quench of the one-dimensional Ising model
with long range interactions between spins at distance
$r$ decaying as $r^{-\alpha}$. For $\alpha =0$, i.e. mean field, all spins
evolve coherently quickly driving the system towards a magnetised state. In the weak long range
regime with $\alpha >1$ there is a coarsening behaviour with competing domains of opposite sign without
development of magnetisation. For strong long range, i.e. $0<\alpha <1$, we show that the system
shows both features, with probability $P_\alpha (N)$ of having the latter one, with the
different limiting behaviours $\lim _{N\to \infty}P_\alpha (N)=0$ (at fixed $\alpha<1$) and
$\lim _{\alpha \to 1}P_\alpha (N)=1$ (at fixed finite $N$). {\color{red}We discuss how this behaviour is a manifestation
of an underlying dynamical scaling symmetry due to the presence of a single characteristic
time $\tau _\alpha (N)\sim N^\alpha$.
