Related Experiment Video
Updated: Jun 26, 2025
08:55
Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses
Published on: June 7, 2018
8.5K
Aging following a zero-temperature quench in the d=3 Ising model.
Denis Gessert1,2, Henrik Christiansen1, Wolfhard Janke1
1Institut für Theoretische Physik, Universität Leipzig, IPF 231101, 04081 Leipzig, Germany.
Physical Review. E
|May 17, 2024
Summary
Aging in the 3D Ising model was studied using Monte Carlo simulations. Researchers found the autocorrelation exponent (λ) to be 1.58(14), which aligns with theoretical bounds, contradicting previous findings.
Area of Science:
- Statistical physics
- Condensed matter physics
- Computational physics
Background:
- Phase-ordering kinetics describes how systems with multiple equilibrium states evolve over time.
- The 3D Ising model is a fundamental model in statistical mechanics used to study magnetism and phase transitions.
- Dynamical scaling and power-law decay are key concepts in understanding the temporal evolution of critical systems.
Purpose of the Study:
- To investigate the aging dynamics in the 3D Ising model after a rapid temperature quench.
- To determine the autocorrelation exponent (λ) and compare it with theoretical bounds, particularly the Fisher-Huse bound.
- To resolve discrepancies with previous studies regarding the violation of universality below the roughening transition.
Main Methods:
- Utilizing large-scale Monte Carlo simulations to model the 3D Ising model.
- Analyzing the two-time spin-spin autocorrelator (C_ag) to probe aging phenomena.
- Employing systematic fitting procedures with various Ansätze to determine the autocorrelation exponent (λ) and its uncertainties.
Main Results:
- The calculated autocorrelation exponent (λ) was found to be 1.58(14).
- This value is consistent with the lower Fisher-Huse bound (λ ≥ d/2 = 1.5).
- The results challenge previous reports suggesting a violation of universality below the roughening transition.
Conclusions:
- The study provides strong evidence that the 3D Ising model does not violate the Fisher-Huse bound for the autocorrelation exponent during aging.
- The findings suggest that universality is maintained in this model under the studied conditions.
- Further research may be needed to fully understand the implications for critical phenomena and phase-ordering kinetics.
Related Concept Videos
02:39Phase Transitions: Melting and Freezing
12.4K
Heating a crystalline solid increases the average energy of its atoms, molecules, or ions, and the solid gets hotter. At some point, the added energy becomes large enough to partially overcome the forces holding the molecules or ions of the solid in their fixed positions, and the solid begins the process of transitioning to the liquid state or melting. At this point, the temperature of the solid stops rising, despite the continual input of heat, and it remains constant until all of the solid is...
12.4K
01:14Atomic Nuclei: Nuclear Spin State Population Distribution
971
Near absolute zero temperatures, in the presence of a magnetic field, the majority of nuclei prefer the lower energy spin-up state to the higher energy spin-down state. As temperatures increase, the energy from thermal collisions distributes the spins more equally between the two states. The Boltzmann distribution equation gives the ratio of the number of spins predicted in the spin −½ (N−) and spin +½ (N+) states.
971
01:14Zeroth Law of Thermodynamics
5.0K
Experimentally, if object A is in equilibrium with object B, and object B is in equilibrium with object C, then object A is in equilibrium with object C. That statement of transitivity is called the "zeroth law of thermodynamics." For example, a cold metal block and a hot metal block are both placed on a metal plate at room temperature. Eventually, the cold block and the plate will be in thermal equilibrium. In addition, the hot block and the plate will be in thermal equilibrium.
5.0K
01:23Atomic Nuclei: Nuclear Relaxation Processes
648
In the absence of an external magnetic field, nuclear spin states are degenerate and randomly oriented. When a magnetic field is applied, the spins begin to precess and orient themselves along (lower energy) or against (higher energy) the direction of the field. At equilibrium, a slight excess population of spins exists in the lower energy state. Because the direction of the magnetic field is fixed as the z-axis, the precessing magnetic moments are randomly oriented around the z-axis.
648
01:28Atomic Nuclei: Types of Nuclear Relaxation
293
Nuclear relaxation restores the equilibrium population imbalance and can occur via spin–lattice or spin–spin mechanisms, which are first-order exponential decay processes.
In spin–lattice or longitudinal relaxation, the excited spins exchange energy with the surrounding lattice as they return to the lower energy level. Among several mechanisms that contribute to spin–lattice relaxation, magnetic dipolar interactions are significant. Here, the excited nucleus transfers...
In spin–lattice or longitudinal relaxation, the excited spins exchange energy with the surrounding lattice as they return to the lower energy level. Among several mechanisms that contribute to spin–lattice relaxation, magnetic dipolar interactions are significant. Here, the excited nucleus transfers...
293
02:11Effects of Temperature on Free Energy
25.5K
The spontaneity of a process depends upon the temperature of the system. Phase transitions, for example, will proceed spontaneously in one direction or the other depending upon the temperature of the substance in question. Likewise, some chemical reactions can also exhibit temperature-dependent spontaneities. To illustrate this concept, the equation relating free energy change to the enthalpy and entropy changes for the process is considered:
25.5K