LATTICE GAS ANALOGUE OF SK MODEL: A paradigm for the glass transition

We investigate the connection between the well known SherringtonKirkpatrick Ising Spin Glass and the correspondent Lattice Gas model by analyzing the relation between their thermodynamical functions. We present results of replica approach in the Replica Symmetric approximation and discuss its stability as a function of temperature and external source. Next we examine the effects of first order Replica Symmetry Breaking at zero temperature. We finally compare SK results with ours and suggests how the latter could be relevant to a description of the structural glass transition. ROM2F/97/44 Submitted to Journal of Physics A 1 Figure caption Figure 1 External field g versus parameter x (x ≡ erf−1(q)) as results from the last of (26). Figure 2 Free energy density versus external field at zero temperature in the replica symmetric solution. The transition point is where the two lower branches cross one each-other. The higher branch is an unstable solution. Figure 3 Replica symmetric order parameter q (= ρ = 〈τ〉 ) at T = 0 as a function of external field. Figure 4 Behaviour of γ0 (= limT→0 β(〈τ 2〉 − 〈τ〉2) ), in the replica symmetric solution, as a function of external field. Figure 5 Replica symmetric order parameter ρ as function of temperature for several values of external field. From top to bottom the values of g are 0.5, 0, −0.6, −0.68, −0.7 and −0.75. The embedded picture represents a magnification of the region around the transition. Figure 6 Replica symmetric order parameter q as function of temperature for several values of external field. From top to bottom the values of g are 0.5, 0, −0.6, −0.68, −0.7 and −0.75. The embedded picture represents a magnification of the region around the transition. Figure 7 Differential susceptibility χ = ∂ρ/∂g as a function of temperature for g = −0.7. Figure 8 Phase diagram for the replica symmetric solution on the plane (g;T ). A line of first order phase transitions ends with a second order transition point. II Figure 9 Behaviour of Λ5 (= 2T λ5) as function of temperature for several values of external field. From bottom to top the values of g are −0.6, −0.68, −0.7 and −0.75. The embedded picture represents a magnification of the region around the transition. Figure 10 Limits of stability of the replica symmetric solution superimposed on its phase diagram. The region under the instability line is the Spin Glass Phase. Figure 11 Free energy density versus external field at zero temperature with first order replica symmetry breaking. The first order transition point is at g = −0.625. Figure 12 Behaviour of μ (= limT→0 βm) as a function of external field. Figure 13 Solution with first order replica symmetry breaking: Off-diagonal order parameter q (= q0) at T = 0 versus external field. Figure 14 Solution with first order replica symmetry breaking: Symmetry breaking parameter d (= q1 − q0) as a function of external field at zero temperature. Figure 15 Solution with first order replica symmetry breaking: Behaviour of γ (= limT→0 β(ρ− q1)) as a function of external field.