Theory of spin glasses

Ultrametricity in the Edwards-Anderson Model

“…In this Letter we study the Edwards-Anderson model [11] for the spin glass in the three-dimensional cubic lattice with J random interactions (for a numerical study in four dimensions, see [12]). With a multispin coding and a parallel-tempering algorithm we numerically investigate the distribution of the overlaps: all the parameters used in the simulations are reported in Table I.…”

Spin Glasses. Still Complex After All These Years?

“…The modern theory of spin glasses began with the work of Edwards and Anderson (EA) [17], who proposed that the essential physics of spin glasses lay not in the details of their microscopic interactions but rather in the competition between quenched ferromagnetic and antiferromagnetic interactions. It should therefore be sufficient to study the Hamiltonian…”

Noncommutative probability in classical disordered systems

“…In these papers the new procedure, called the noncommutative replica procedure, which is an analog of the replica procedure of Edwards and Anderson [16], was proposed to describe the statistical mechanics of quenched disordered systems (for example, spin glasses).…”

“…We will not discuss here the standard replica approach, see for introduction to spin glasses and the replica method [16], [17], [18].…”