Dynamics of a mean spherical model with competing interactions

Abstract

The Langevin dynamics of a $d$-dimensional mean spherical model with competing interactions along $m\le d$ directions of a hypercubic lattice is analysed. After a quench at high temperatures, the dynamical behaviour is characterized by two distinct time scales associated with stationary and aging regimes. The asymptotic expressions for the autocorrelation and response functions, in supercritical, critical, and subcritical cases, were calculated. Aging effects, which are known to be present in the ferromagnetic version of this model system, are not affected by the introduction of competing interactions.

References in corpus (2)

• Response of non-equilibrium systems at criticality: Ferromagnetic models in dimension two and above
• Dynamics of ferromagnetic spherical spin models with power law interactions: exact solution

Cited by in corpus (15)

• Quantum phase transition in the spin-anisotropic quantum spherical model
• Spherical model of growing interfaces
• Lindblad dynamics of the quantum spherical model
• Axiomatic construction of quantum Langevin equations
• Quantum aging and dynamical universality in the long-range $O(N\to \infty )$ model
• Non-local meta-conformal invariance, diffusion-limited erosion and the XXZ chain
• The fluctuation-dissipation theorem and the linear Glauber model
• Non-equilibrium relaxations: ageing and finite-size effects
• Asymmetric Langevin dynamics for the ferromagnetic spherical model
• Aging and fluctuation-dissipation ratio in a nonequilibrium $q$-state lattice model
• Approach to equilibrium for a class of random quantum models of infinite range
• Stochastic Quantization of the Spherical Model and Supersymmetry
• Dynamical symmetries in the non-equilibrium dynamics of the directed spherical model
• Schrödinger-invariance in the voter model
• The frustrated spherical model: an alternative to Ginzburg-Landau Hamiltonians with competing interactions