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We consider a Kuramoto model of coupled oscillators that includes quenched random interactions of the type used by van Hemmen in his model of spin glasses. The phase diagram is obtained analytically for the case of zero noise and a Lorentzian distribution of the oscillators natural frequencies. Depending on the size of the attractive and random coupling terms, the system displays four states: complete incoherence, partial synchronization, partial antiphase synchronization, and a mix of antiphase and ordinary synchronization.
The Kuramoto model describes a system of globally coupled phase-only oscillators with distributed natural frequencies. The model in the steady state exhibits a phase transition as a function of the coupling strength, between a low-coupling incoherent
In the present work it is studied the fermionic van Hemmen model for the spin glass (SG) with a transverse magnetic field $Gamma$. In this model, the spin operators are written as a bilinear combination of fermionic operators, which allows the analys
Using the main results of the Kuramoto theory of globally coupled phase oscillators combined with methods from probability and generalized function theory in a geometric analysis, we extend Kuramotos results and obtain a mathematical description of t
The one-parametric Wang-Landau (WL) method is implemented together with an extrapolation scheme to yield approximations of the two-dimensional (exchange-energy, field-energy) density of states (DOS) of the 3D bimodal random-field Ising model (RFIM).
We analyze the Eckhaus instability of plane waves in the one-dimensional complex Ginzburg-Landau equation (CGLE) and describe the nonlinear effects arising in the Eckhaus unstable regime. Modulated amplitude waves (MAWs) are quasi-periodic solutions