Critical Behavior of Ising Model wit(经典3篇)
Critical Behavior of Ising Model with External Field: An Introduction to the Concept
篇一
The Ising model is a mathematical model used in statistical mechanics to study the behavior of magnetic systems. It was proposed by Ernst Ising in 1925, and since then, it has been extensively studied and applied in various fields, ranging from physics to computer science.
The Ising model consists of a lattice of spins, which can be thought of as tiny magnets that can point either up or down. The spins interact with their nearest neighbors, and the goal is to understand how the system behaves as a whole.
In its simplest form, the Ising model does not include any external influences. However, in many cases, an external field is present, which can affect the behavior of the system significantly. This external field can be thought of as an additional magnetic field that acts on the spins.
When an external field is introduced, the Ising model exhibits critical behavior. Critical behavior refers to the phenomenon where the system undergoes a phase transition at a critical temperature. In the case of the Ising model, this phase transition is from a magnetized state to a non-magnetized state.
At temperatures below the critical temperature, the spins tend to align with the external field, resulting in a magnetized state. On the other hand, at temperatures above the critical temperature, the spins become disordered and point in random directions, leading to a non-magnetized state.
The critical behavior of the Ising model with an external field can be studied using various techniques, such as mean-field theory, Monte Carlo simulations, and renormalization group methods. These methods allow researchers to understand the properties of the system near the critical temperature and predict its behavior.
One of the key quantities used to describe the critical behavior of the Ising model is the order parameter. The order parameter is a measure of the degree of magnetization in the system. Near the critical temperature, the order parameter exhibits power-law scaling, which is a characteristic feature of critical behavior.
Understanding the critical behavior of the Ising model with an external field is not only important for theoretical reasons but also has practical implications. For example, it can help in the design of magnetic materials with specific properties or in understanding the behavior of magnetic systems in the presence of external influences.
In conclusion, the Ising model with an external field exhibits critical behavior, where the system undergoes a phase transition from a magnetized state to a non-magnetized state at a critical temperature. Studying the critical behavior of the Ising model is crucial for understanding the behavior of magnetic systems and has both theoretical and practical implications.
篇二
Critical Behavior of Ising Model with External Field: Experimental Evidence and Applications
The Ising model with an external field is not only a topic of theoretical interest but also has practical applications in various fields. In this article, we will explore some of the experimental evidence for the critical behavior of the Ising model with an external field and discuss its applications.
Experimental evidence for the critical behavior of the Ising model with an external field can be obtained through various techniques. One common approach is to study magnetic materials that exhibit similar behavior to the Ising model. By manipulating the external field and measuring the magnetization of the material, researchers can observe the phase transition and critical behavior.
For example, in a study conducted by Wang et al. (2018), the critical behavior of a magnetic material was investigated using a superconducting quantum interference device (SQUID). The material exhibited a phase transition from a magnetized state to a non-magnetized state at a critical temperature, consistent with the predictions of the Ising model.
Another experimental technique used to study the critical behavior of the Ising model is neutron scattering. Neutron scattering experiments allow researchers to probe the magnetic properties of materials at a microscopic level. By analyzing the scattering patterns, researchers can extract information about the correlation length and critical exponents, which are important quantities characterizing critical behavior.
The critical behavior of the Ising model with an external field has applications in various fields, including materials science and condensed matter physics. For example, understanding the critical behavior can help in the design and development of materials with specific magnetic properties. By manipulating the external field and temperature, it is possible to control the magnetization of a material, which has implications for applications such as data storage and magnetic sensors.
Furthermore, the Ising model with an external field can be used to study other complex systems, such as social networks and neural networks. By mapping these systems onto the Ising model, researchers can gain insights into their behavior and make predictions about their critical behavior.
In conclusion, experimental evidence supports the critical behavior of the Ising model with an external field. Techniques such as SQUID measurements and neutron scattering allow researchers to observe the phase transition and study the critical behavior of magnetic materials. The understanding of the critical behavior has applications in materials science and other fields, providing insights into the behavior of complex systems.
Critical Behavior of Ising Model wit 篇三
Critical Behavior of Ising Model with Long Range Correlated Quenched Impurities
The theoretic renormalization-group approach is applied to the study of the critical behavior of the ddimensional Ising model with long-range correlated quenched impurities, which has a power-like correlations r-(d-ρ).The asymptotic scaling law is studied in the framework of the expansion in ε = 4 - d. In d ＜ 4, the dynamic exponent z .is calculated up to the second order in ρ with ρ = O(ε1/2). The shape function is obtained in one-loop calculation.When d = 4, the logarithmic corrections to the critical behavior are found. The finite size effect on the order parameter relaxation rate is also studied.
作 者： CHEN Yuan 作者单位： Department of Physics, Guangzhou University, Guangzhou 510405, China 刊 名：理论物理通讯(英
