In mathematical physics, a lattice model is a mathematical model of a physical system that is defined on a lattice, as opposed to a continuum, such as the continuum of space or spacetime. Lattice models originally occurred in the context of condensed matter physics, where the atoms of a crystal automatically form a lattice. Currently, lattice models are quite popular in theoretical physics, for many reasons. Some models are exactly solvable, and thus offer insight into physics beyond what can be learned from perturbation theory. Lattice models are also ideal for study by the methods of computational physics, as the discretization of any continuum model automatically turns it into a lattice model. The exact solution to many of these models (when they are solvable) includes the presence of s
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| - Gittermodell (de)
- Lattice model (physics) (en)
- 격자 모형 (ko)
- Решёточная модель (физика) (ru)
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| - Gittermodelle sind im Allgemeinen mathematische Modelle, bei denen die Freiheitsgrade des Systems den Elementen eines Gitters, d. h. einer abzählbaren Menge von Punkten, zugeordnet sind. Das unterscheidet sie von Kontinuumsmodellen, bei denen jedem Wert eines Intervalls Freiheitsgrade zugeordnet sind. Typische Beispiele sind die Beschreibung der Magnetisierung eines Festkörpers durch an den als fix und periodisch angenommenen Orten der Atomkerne lokalisierte Spins (z. B. Ising-Modell) oder der Bewegung der Leitungselektronen durch das Springen zwischen an den Orten der Atomkerne lokalisierten Orbitalen (Hubbard-Modell). Das Modell dient zur näherungsweisen Beschreibung des physikalischen Systems. (de)
- In mathematical physics, a lattice model is a mathematical model of a physical system that is defined on a lattice, as opposed to a continuum, such as the continuum of space or spacetime. Lattice models originally occurred in the context of condensed matter physics, where the atoms of a crystal automatically form a lattice. Currently, lattice models are quite popular in theoretical physics, for many reasons. Some models are exactly solvable, and thus offer insight into physics beyond what can be learned from perturbation theory. Lattice models are also ideal for study by the methods of computational physics, as the discretization of any continuum model automatically turns it into a lattice model. The exact solution to many of these models (when they are solvable) includes the presence of s (en)
- 격자 모형(格子模型, 영어: lattice model 래티스 모델[*])이란 물리학 용어로, 공간 또는 시공의 연속체에 대립하는 격자에서 정의된 물리학적인 모형을 말한다. 격자 모형은 최초에 응집물질물리학의 문맥에서 발생했다. 거기서 결정의 원자는 격자를 자동적으로 형성한다. 현재, 많은 이유 때문에 격자 모형은 이론물리학에서 아주 인기가 있다. 일부 모델은 정확하게 해결할 수 있고, 따라서 섭동 이론으로부터 배우게 될 수 있는 것을넘어 물리학에 대한 통찰을 제공한다. 격자 모형은 또한 계산물리학적 방법의 연구에 이상적이고, 어떠한 연속적인 모형의 불연속화도 자동적으로 격자 모형로 변한다. 응집물질물리학에서 등장하는 격자 모형은 이징 모형, 포츠 모형, XY 모형, 도다 격자 등이 있다. 이러한 모형들은 보통 적분가능계로서 해석적으로 완전히 풀 수 있고, 보통 솔리톤을 가진다. 이러한 격자 모형을 풀기 위하여 (inverse-scattering transform)과 럭스 쌍, 양-백스터 방정식, 양자군 등을 사용한다. 이러한 모형의 해답은 자연에서 상전이, 자화율과 비례 축소(scaling) 행동뿐만 아니라, 또한 양자장론의 성질에 대한 통찰까지 주었다. (ko)
- Решёточная модель — физическая или даже математическая модель, определённая на дискретной решётке, в противоположность непрерывному континууму пространства или пространства-времени. Решёточные модели изначально появились в контексте физики конденсированного состояния, когда атомы кристалла самостоятельно формируют кристаллическую решётку. (ru)
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| - Gittermodelle sind im Allgemeinen mathematische Modelle, bei denen die Freiheitsgrade des Systems den Elementen eines Gitters, d. h. einer abzählbaren Menge von Punkten, zugeordnet sind. Das unterscheidet sie von Kontinuumsmodellen, bei denen jedem Wert eines Intervalls Freiheitsgrade zugeordnet sind. Typische Beispiele sind die Beschreibung der Magnetisierung eines Festkörpers durch an den als fix und periodisch angenommenen Orten der Atomkerne lokalisierte Spins (z. B. Ising-Modell) oder der Bewegung der Leitungselektronen durch das Springen zwischen an den Orten der Atomkerne lokalisierten Orbitalen (Hubbard-Modell). Das Modell dient zur näherungsweisen Beschreibung des physikalischen Systems. Gittermodelle kommen beispielsweise zum Einsatz, wenn Wechselwirkungen zwischen Körpern beschrieben werden, deren räumliche Freiheitsgrade derart eingeschränkt sind, dass sie sich nur an den Gitterpunkten aufhalten können, bzw. dass die darüber hinaus verbleibende Variabilität nicht zu relevanten Änderungen des zu simulierenden Systems führt.Die Darstellung als Gittermodell kann zu einer erheblichen Vereinfachung der notwendigen Berechnungen führen. (de)
- In mathematical physics, a lattice model is a mathematical model of a physical system that is defined on a lattice, as opposed to a continuum, such as the continuum of space or spacetime. Lattice models originally occurred in the context of condensed matter physics, where the atoms of a crystal automatically form a lattice. Currently, lattice models are quite popular in theoretical physics, for many reasons. Some models are exactly solvable, and thus offer insight into physics beyond what can be learned from perturbation theory. Lattice models are also ideal for study by the methods of computational physics, as the discretization of any continuum model automatically turns it into a lattice model. The exact solution to many of these models (when they are solvable) includes the presence of solitons. Techniques for solving these include the inverse scattering transform and the method of Lax pairs, the Yang–Baxter equation and quantum groups. The solution of these models has given insights into the nature of phase transitions, magnetization and scaling behaviour, as well as insights into the nature of quantum field theory. Physical lattice models frequently occur as an approximation to a continuum theory, either to give an ultraviolet cutoff to the theory to prevent divergences or to perform numerical computations. An example of a continuum theory that is widely studied by lattice models is the QCD lattice model, a discretization of quantum chromodynamics. However, digital physics considers nature fundamentally discrete at the Planck scale, which imposes upper limit to the density of information, aka Holographic principle. More generally, lattice gauge theory and lattice field theory are areas of study. Lattice models are also used to simulate the structure and dynamics of polymers. (en)
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