The Validity of Classical Nucleation Theory for Ising Models
نویسندگان
چکیده
While the classical nucleation theory (CNT) is widely used to predict the rate of first-order phase transitions, its validity has been questioned due to discrepancies with experiments. We systematically test the individual components of CNT by computer simulations of the Ising models and confirm its fundamental assumptions under a wide range of conditions (h = 0.01-0.13 J, T = 0.44-0.84 Tc in 2D and h = 0.30-0.60 J, T = 0.48-0.62 Tc in 3D). First, CNT accurately predicts the nucleation rate if the correct droplet free energy is provided. Furthermore, theoretical prediction of droplet free energy matches numerical results very well in the 2D Ising model, if appropriate correction terms are added. This establishes the 2D Ising model as an important reference point where existing theories can predict nucleation rate accurately with no adjustable parameters.
منابع مشابه
Validity of classical nucleation theory for Ising models.
While the classical nucleation theory (CNT) is widely used to predict the rate of first-order phase transitions, its validity has been questioned due to discrepancies with experiments. We systematically test the individual components of CNT by computer simulations of the Ising models and confirm its fundamental assumptions under a wide range of conditions ( h=0.01-0.13J , T=0.44-0.84Tc in two-d...
متن کاملNumerical tests of nucleation theories for the Ising models.
The classical nucleation theory (CNT) is tested systematically by computer simulations of the two-dimensional (2D) and three-dimensional (3D) Ising models with a Glauber-type spin flip dynamics. While previous studies suggested potential problems with CNT, our numerical results show that the fundamental assumption of CNT is correct. In particular, the Becker-Döring theory accurately predicts th...
متن کاملNucleation and hysteresis in Ising model: Classical theory versus computer simulation
We have studied the nucleation in the nearest neighbour ferromagnetic Ising model, in different (d) dimensions, by extensive Monte Carlo simulation using the heat-bath dynamics. The nucleation time (τ) has been studied as a function of the magnetic field (h) for various system sizes in different dimensions (d = 2, 3, 4). The logarithm of the nucleation time is found to be proportional to the po...
متن کاملHigh order perturbation study of the frustrated quantum Ising chain
In this paper, using high order perturbative series expansion method, the critical exponents of the order parameter and susceptibility in transition from ferromagnetic to disordered phases for 1D quantum Ising model in transverse field, with ferromagnetic nearest neighbor and anti-ferromagnetic next to nearest neighbor interactions, are calculated. It is found that for small value of the frustr...
متن کاملPrecipitation in Al-Zr-Sc alloys: a comparison between kinetic Monte Carlo, cluster dynamics and classical nucleation theory
Zr and Sc precipitate in aluminum alloys to form the Al3ZrxSc1−x compound which, for low supersaturations of the solid solution, exhibits the L12 structure. The aim of the present study is to model at an atomic scale the kinetics of precipitation and to build mesoscopic models so as to extend the range of supersaturations and annealing times that can be simulated up to values of practical inter...
متن کامل