Relation between gap and order in spin model

In summary, "gap" and "order" in a spin model refer to the energy difference between the ground state and first excited state, and the degree of arrangement and correlation between spins in the system, respectively. These two concepts are closely related, with a larger gap indicating a higher degree of order. The gap and order are dynamic and can change over time, and various techniques such as neutron scattering and numerical simulations are used to measure them. Studying the relation between gap and order in spin models has practical applications in designing new materials and understanding complex systems with potential uses in technology and medicine.
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what is the definition of spin gap?I may have ever heard a conclusion that spin gap will not exist while the system present long range order(right?),but the system of XXZ model in external field could stay in ferromagnetic phase,and have a long range order with a gapped excitation.why?
 
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One more question appended.What is the order parameter of XXZ chain model in external field to distinguish between XY phase and ferromagnetic phase? Magnetization? but order parameter has a value of 0 for disorder phase,value of 1 for complete order phase...
 
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The relation between gap and order in a spin model is a complex and ongoing area of research in the field of condensed matter physics. The concept of spin gap refers to the energy difference between the ground state and the lowest excited state of a system with spin degrees of freedom.

In general, the presence of a spin gap is associated with a lack of long-range order in the system, as the energy required to break the gap and create excitations is too high for them to form spontaneously. However, as mentioned, there are exceptions to this rule, such as in the XXZ model with an external field.

In this case, the external field acts to stabilize the ferromagnetic phase, which is characterized by long-range order. This means that the spins in the system are aligned in a particular direction, and this alignment persists even at long distances. The presence of a spin gap in this system is due to the conservation of total spin in the presence of the external field, which restricts the possible excitations that can occur.

In summary, the relation between gap and order in spin models is a complex and nuanced one, and it is important to consider the specific details of each system when studying this relationship. The definition of spin gap is the energy difference between the ground state and the lowest excited state in a system with spin degrees of freedom. While it is generally true that a spin gap is associated with a lack of long-range order, there are exceptions to this rule, such as in the XXZ model with an external field.
 

1. What is the concept of "gap" and "order" in a spin model?

In a spin model, "gap" refers to the energy difference between the ground state and the first excited state of the system. "Order" is a measure of how the spins in the system are arranged and correlated with each other. It can indicate whether the system is in a well-organized state or a disordered state.

2. How are gap and order related in a spin model?

In a spin model, the gap and order are closely related. In general, a larger gap indicates a higher degree of order in the system. This is because a larger gap means the spins are more stable and less likely to fluctuate, leading to a more organized and ordered state.

3. Can the gap and order in a spin model change over time?

Yes, the gap and order in a spin model can change over time. This is due to the dynamic nature of spin systems, where the spins can interact with each other and change their orientations. The changes in the gap and order can be affected by external factors such as temperature and magnetic fields.

4. How do researchers measure the gap and order in a spin model?

There are various techniques for measuring the gap and order in a spin model, such as neutron scattering, magnetic resonance, and numerical simulations. These methods involve analyzing the energy levels and spin configurations of the system to determine the gap and order.

5. What are some real-world applications of studying the relation between gap and order in spin models?

Studying the relation between gap and order in spin models has many practical applications. For example, it can help researchers understand and design new materials with specific magnetic properties for use in data storage and spintronics. It can also provide insights into the behavior of complex systems, such as magnetic materials and quantum systems, which have applications in various fields such as technology and medicine.

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