Elusive spin-glass phase in the random field Ising model

Area of Science:

• Statistical Mechanics
• Condensed Matter Physics
• Disordered Systems

Background:

• The random field Ising model (RFIM) is a fundamental model in statistical mechanics used to study disordered magnetic systems.
• Understanding the conditions for the emergence of different phases, such as ferromagnetic and spin-glass phases, is crucial for characterizing magnetic materials.

Purpose of the Study:

• To rigorously investigate the existence of a spin-glass phase in the random field Ising model under equilibrium conditions.
• To explore the possibility of a spin-glass phase when the system's magnetization is externally controlled.

Main Methods:

• Rigorous mathematical analysis of the spin-glass susceptibility in the RFIM.
• Explicit demonstration of a spin-glass phase on the Bethe lattice for fixed magnetization values.

Main Results:

• The spin-glass susceptibility is rigorously shown to be bounded by the ferromagnetic susceptibility in equilibrium.
• This implies that no equilibrium spin-glass phase can exist outside the ferromagnetic critical line.
• A spin-glass phase is explicitly shown to exist on the Bethe lattice when magnetization is fixed below its equilibrium value.

Conclusions:

• The equilibrium phase diagram of the RFIM is constrained, preventing spin-glass phases away from the ferromagnetic critical line.
• The study highlights the importance of boundary conditions and external control in potentially stabilizing exotic phases like spin-glasses in disordered systems.