Ising model

About: Ising model is a research topic. Over the lifetime, 25508 publications have been published within this topic receiving 555000 citations.

Antiferromagnetic critical point on graphene's honeycomb lattice: A functional renormalization group approach

Abstract: Electrons on the half-filled honeycomb lattice are expected to undergo a direct continuous transition from the semimetallic into the antiferromagnetic insulating phase with increase of on-site Hubbard repulsion We attempt to further quantify the critical behavior at this quantum phase transition by means of functional renormalization group (RG), within an effective Gross-Neveu-Yukawa theory for an SO(3) order parameter ("chiral Heisenberg universality class") Our calculation yields an estimate of the critical exponents $ u \simeq 131$, $\eta_\phi \simeq 101$, and $\eta_\Psi \simeq 008$, in reasonable agreement with the second-order expansion around the upper critical dimension To test the validity of the present method we use the conventional Gross-Neveu-Yukawa theory with Z(2) order parameter ("chiral Ising universality class") as a benchmark system We explicitly show that our functional RG approximation in the sharp-cutoff scheme becomes one-loop exact both near the upper as well as the lower critical dimension Directly in 2+1 dimensions, our chiral-Ising results agree with the best available predictions from other methods within the single-digit percent range for $ u$ and $\eta_\phi$ and the double-digit percent range for $\eta_\Psi$ While one would expect a similar performance of our approximation in the chiral Heisenberg universality class, discrepancies with the results of other calculations here are more significant Discussion and summary of various approaches is presented

Absence of first-order transition and tricritical point in the dynamic phase diagram of a spatially extended bistable system in an oscillating field.

Abstract: It has been well established that spatially extended, bistable systems that are driven by an oscillating field exhibit a nonequilibrium dynamic phase transition (DPT). The DPT occurs when the field frequency is of the order of the inverse of an intrinsic lifetime associated with the transitions between the two stable states in a static field of the same magnitude as the amplitude of the oscillating field. The DPT is continuous and belongs to the same universality class as the equilibrium phase transition of the Ising model in zero field [G. Korniss et al., Phys. Rev. E 63, 016120 (2001); H. Fujisaka et al., Phys. Rev. E 63, 036109 (2001)]. However, it has previously been claimed that the DPT becomes discontinuous at temperatures below a tricritical point [M. Acharyya, Phys. Rev. E 59, 218 (1999)]. This claim was based on observations in dynamic Monte Carlo simulations of a multipeaked probability density for the dynamic order parameter and negative values of the fourth-order cumulant ratio. Both phenomena can be characteristic of discontinuous phase transitions. Here we use classical nucleation theory for the decay of metastable phases, together with data from large-scale dynamic Monte Carlo simulations of a two-dimensional kinetic Ising ferromagnet, to show that these observations in this case are merely finite-size effects. For sufficiently small systems and low temperatures, the continuous DPT is replaced, not by a discontinuous phase transition, but by a crossover to stochastic resonance. In the infinite-system limit, the stochastic-resonance regime vanishes, and the continuous DPT should persist for all nonzero temperatures.

Uniaxial relaxor ferroelectrics: The ferroic random-field Ising model materialized at last

Abstract: Owing to their intrinsic charge disorder ferroelectric crystals of strontium-barium-niobate doped with Ce3+ materialize the three-dimensional ferroic random-field Ising model (RFIM) as evidenced by order paramenter and susceptibility criticalities with 93Nb NMR and dielectric spectroscopy, respectively. Upon cooling towards Tc, extreme critical slowing-down due to activated dynamic scaling gives rise to relaxor-like dispersion of the susceptibility and to a metastable ferroelectric nanodomain state with fractal size distribution as imaged by piezoelectric force microscopy.

Spin-3/2 Ising model for tricritical points in ternary fluid mixtures

Abstract: We present a lattice-gas model of ternary fluid mixtures. Within the mean-field approximation, we study a nonsymmetric tricritical point in this model. We compare our results to the experimental observations on the system ethanol-water-carbon-dioxide. In the course of our work, we have studied a Landau theory describing the neighborhood of a fourth-order critical point. Also, we have noted that mean-field theory indicates the existence of a fourth-order critical point in the spin-1 model of Blume, Emery, and Griffiths, corresponding to $Kl0$, $J+Kg0$.

The Continuous-Spin, Ising Model of Field Theory and the Renormalization Group

Abstract: This paper sketches briefly the ideas of the ferromagnetic critical point, or bifurcation point, as exemplified in the Ising model. Historically, the only reliable, general methods available to attack this problem have been series expansion methods. The development of scaling ideas and the realization that Euclidean, Boson, quantum field-theory is the same problem as the scaling limit of critical phenomena has led to the development of the renormalization group approach to critical phenomena. For clarity, attention is focused on that continuous- spin Ising model which is equivalent to a g0:ɸ4:d field theory. A review of the ideas of the renormalization group approach in statistical mechanical language shows that the key assumption is that the limits as the bare coupling-constant goes to infinity and the ultra-violet cut-off is removed are independent of order. Calculations show that this assumption is satisfied in one and two dimensions, but fails in three and four dimensions where the renormalized coupling-constant is not a monotonic function of the bare coupling constant. The renormalization group approach to critical phenomena is seen as a theory of the maximum of the renormalized coupling-constant which may, or may not, be a theory of the Ising-model critical-point.