Temperature chaos as a logical consequence of the reentrant transition in spin glasses

TL;DR

This paper develops a correlated-disorder formulation for the finite‑dimensional Edwards–Anderson spin glass and reveals a logical link between reentrance and temperature chaos. By introducing a three-parameter phase diagram in $(\\gamma,\\beta_p,1/\\beta)$ and analyzing limiting cross-sections ($\\beta_p=0$, $\\gamma\\to\\infty$, and $\\gamma=0$), it shows that, if a finite‑temperature spin-glass phase exists, the ferromagnet–spin-glass boundary is nonreentrant when temperature chaos is absent, and reentrance implies temperature chaos. The framework recovers standard EA and Nishimori-line limits, connects to Kitatani's model, and generalizes to Gaussian disorder and related gauge models, providing a symmetry-based basis for understanding spin-glass phenomenology beyond mean-field.

Abstract

Temperature chaos is a striking phenomenon in spin glasses, where even slight changes in temperature lead to a complete reconfiguration of the spin state. Another intriguing effect is the reentrant transition, in which lowering the temperature drives the system from a ferromagnetic phase into a less ordered spin-glass or paramagnetic phase. In the present paper, we reveal an unexpected connection between these seemingly unrelated phenomena in the finite-dimensional Edwards-Anderson model of spin glasses by introducing a generalized formulation that incorporates correlations among disorder variables. Assuming the existence of a spin glass phase at finite temperature, we establish that temperature chaos arises as a logical consequence of reentrance in the Edwards-Anderson model. Our findings uncover a previously hidden mathematical structure relating reentrance and temperature chaos, offering a new perspective on the physics of spin glasses beyond the mean-field theory.

Figures (11)

• Figure 1: Schematic phase diagram for $\beta_p = 0$, showing a cross section of the 3D phase diagram in Figs. \ref{['fig:3D_NoTC_NoReent']} and \ref{['fig:3D_TC_Reent']}. The phase boundaries have the same shape as in the Edwards-Anderson model on the same lattice, with $\beta_p$ replaced by $\gamma$. The ferromagnetic phase of the Edwards-Anderson model is replaced by a Mattis-like spin glass phase (M-SG) with vanishing magnetization ($m = 0$). Reentrance is assumed along boundary II, but not along II'. NL denotes the Nishimori line ($\beta = \gamma$). Boundary I indicates the transition between paramagnetic and non-paramagnetic phases. ${\beta_{\rm c0}}^{-1}$ is the critical temperature of the pure Ising model, which is recovered in the limit $\gamma \to \infty$ for gauge-invariant quantities. ${\beta_{\rm g}}^{-1}$ is the spin glass transition temperature of the Edwards-Anderson model recovered at $\gamma=0$.
• Figure 2: Cross section of the phase diagram at $\gamma\to\infty$. $\beta_{c0}$ is the critical inverse temperature of the pure Ising model on the same lattice. The lower left part is the Mattis-like spin glass phase. NL is the Nishimori line $\beta=\beta_p$. Denoted by I is the boundary between the paramagnetic and ferromagnetic/spin glass phases, which is the cross section of the boundary I in the 3D phase diagram in Fig. \ref{['fig:3D_NoTC_NoReent']}. The same applies to III as the boundary between the Mattis-like spin glass and ferromagnetic phases. MCP is the multicritical point.
• Figure 3: Cross section of the phase diagram at $\gamma=0$ when temperature chaos does not exist in the Edwards-Anderson model. MCP is the multicritical point. Denoted by I is the boundary between the paramagnetic and ferromagnetic/spin glass phases, which is the cross section of the boundary I in the 3D phase diagram in Fig. \ref{['fig:3D_NoTC_NoReent']}. The same applies to III as the boundary between the spin glass and ferromagnetic phases. $\beta_{\rm g}^{-1}$ is the spin glass transition temperature of the Edwards-Anderson model.
• Figure 4: Cross section of the phase diagram at $\gamma=0$ under the putative reentrant transition. It is shown in the main text that this structure is not allowed. Point P is on the NL ($\beta=\beta_p$) in the ferromagnetic phase and other points Q, S, and R are in the spin glass phase. Denoted by I is the boundary between the paramagnetic and ferromagnetic/spin glass phases.
• Figure 5: Cross section of the phase diagram at $\gamma=0$ when the multicritical point is below the NL. It is shown in the main text that this structure is not allowed. Each point has the coordinate as: Q$(\beta_p,\beta)$, S$(\beta,\beta_p)$, P$(\beta_p,\beta_p)$, and R$(\beta,\beta)$. P and R are on the NL.

Theorems & Definitions (1)

• Proposition 1