Elementary excitations and the phase transition in the bimodal Ising spin glass model

Abstract

We show how the nature of the the phase transition in the two-dimensional bimodal Ising spin glass model can be understood in terms of elementary excitations. Although the energy gap with the ground state is expected to be 4J in the ferromagnetic phase, a gap 2J is in fact found if the finite lattice is wound around a cylinder of odd circumference L. This 2J gap is really a finite size effect that should not occur in the thermodynamic limit of the ferromagnet. The spatial influence of the frustration must be limited and not wrap around the system if L is large enough. In essence, the absence of 2J excitations defines the ferromagnetic phase without recourse to calculating magnetisation or investigating the system response to domain wall defects. This study directly investigates the response to temperature. We also estimate the defect concentration where the phase transition to the spin glass glass state occurs. The value pc = 0.1045(11) is in reasonable agreement with the literature.

Simple relation between frustration and transition points in diluted spin glasses

“…He reported [27] that the condition v(p) = 1 gives a value of p that is close to the phase-transition point for the model at zero temperature. For instance, the value p 0.1031 yielded from the condition for the square lattice is very close to the actual phase-transition point numerically obtained as p = 0.1033(1) [23] or 0.1045(11) [24]. The good correspondence is found in several two-dimensional lattices and hierarchical lattices [31].…”

“…1 shows. This conjecture was denied by subsequent detailed studies [10,[17][18][19][20][21][22][23][24]. The established phase boundary, however, is almost vertical.…”

Domain-wall excitations in the two-dimensional Ising spin glass

“…87 provides uniform samples, but it is much more demanding computationally, such that only smaller system sizes can be treated reliably. We have studied systems of edge lengths L = 10, 16,20,24,28,32,48,64,80,100, and 128 for this method, using 1000 samples per size and producing ten independent ground-state configurations per sample. Data from this algorithm are labeled "uniform sampling".…”

Spin Glass Phase Exists in the Random Weak Disorder for the Villain Model

“…The two dimensional fully frustrated Ising model, or Villain model [1], consists of Ising spins on a square lattice with nearest neighbor bonds Figure 1. The method is used in the calculation basing on the Pfaffian [5] through a degenerate state perturbation theory [6]- [8]. The degeneracies of the excitated states are calculated from an expression of the eigenvalues with disorder subspace.…”

“…The energy gap is 4J in the mentioned system if L is even. Otherwise it is 2J [4] [5]. In this work, we propose a simple picture of spin glass phase in the weak disorder that has evaluated from power law distribution of first excitations of ground states.…”