14 citations · 45 across the 7 of their papers we have counts for
7 papers
Generalizations of Parisi's replica symmetry breaking and overlaps in random energy models
Bernard Derrida, Peter Mottishaw
The random energy model (REM) is the simplest spin glass model which exhibits replica symmetry breaking. It is well known since the 80's that its overlaps are non-selfaveraging and…
The discrete random energy model and one step replica symmetry breaking
Bernard Derrida, Peter Mottishaw
We solve the random energy model when the energies of the configurations take only integer values. In the thermodynamic limit, the average overlaps remain size dependent and oscill…
One step replica symmetry breaking and overlaps between two temperatures
Bernard Derrida, Peter Mottishaw
We obtain an exact analytic expression for the average distribution, in the thermodynamic limit, of overlaps between two copies of the same random energy model (REM) at different t…
Finite size corrections to the Parisi overlap function in the GREM
Bernard Derrida, Peter Mottishaw
We investigate the effects of finite size corrections on the overlap probabilities in the Generalized Random Energy Model (GREM) in two situations where replica symmetry is broken…
On the genealogy of branching random walks and of directed polymers
Bernard Derrida, Peter Mottishaw
It is well known that the mean field theory of directed polymers in a random medium exhibits replica symmetry breaking with a distribution of overlaps which consists of two delta f…
Finite size corrections in the random energy model and the replica approach
Bernard Derrida, Peter Mottishaw
We present a systematic and exact way of computing finite size corrections for the random energy model, in its low temperature phase. We obtain explicit (though complicated) expres…
An exclusion process on a tree with constant aggregate hopping rate
Peter Mottishaw, Bartlomiej Waclaw, Martin R. Evans
We introduce a model of a totally asymmetric simple exclusion process (TASEP) on a tree network where the aggregate hopping rate is constant from level to level. With this choice f…