Pressure-induced orientational glass phase in molecular para-hydrogen

Abstract

We propose a theoretical description of a possible orientational glass transition in solid molecular para-hydrogen and ortho-deuterium under pressure supposing that they are mixtures of J=0 and J=2 states of molecules. The theory uses the basic concepts and methods of standard spin-glass theory. We expect our orientational glass to correspond to the II' phase of the high-pressure hydrogen phase diagram.

Spin-glass-type state in complex nonmagnetic systems

“…The studies of this model were later continued in our works, in [16], [17], and in the works of Moskalenko with coauthors (see [2] and the references therein). An important development of the model was to study the quadrupole system with J = 2 and the quadrupolar models with multiparticle interaction [18], which are similar to the model proposed in [19] for spin systems. In this case, it became possible to describe the orientational glass phase observed for high pressures in solid molecular ortho-D 2 and para-H 2 [20].…”

Full replica symmetry breaking in p-spin-glass-like systems

“…So there is no reflection symmetry. Behavior of this model is significantly different from what one usually has in the case of Ising-like operators [2,3,18,19,20,21,22,23,24,25,26,28]. We have done earlier calculations of 1RSB solution for various values of p that could change continuously [26].…”

“…Here we propose analytical solution of p-spin-glass-like system and discuss physical applications of this model. For a long time there was a conjecture that there are more or less two classes of models, depending on how the replica symmetry breaking appears [18]. In one class of models full replica symmetry breaking (FRSB) occurs continuously at the transition point from the paramagnetic state to the glass state (like, e.g., in SK model).…”

“…The prime on ′ means that only the superscripts belonging to the same δq are necessarily different. The coefficients of the second and third orders, λ (RS) repl , L, B 3 , ..B 4 , have been obtained earlier [18,26,27], but we also write them in Supplementary Material for readability. This is the only overlap with our previous publications.…”

“…Replacing the simple Ising spins by more complex operatorsÛ dramatically expands the range of solvable tasks. The operatorÛ can be, for example, the axial quadrupole moment (quadrupole glass in molecular solid hydrogen at different pressures) or the role ofÛ can be played by certain combinations of the cubic harmonics (orientational glass of the clusters, for example, in C 60 in a wide pressure range), see [18,19,20,21,22,23,24,25,26].…”