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supratimmitra
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can anybody tell me why in general phase transition is not possible in one dimension? and for a lattice gas at low temp. why it requires long range order to occur phase transition?
In one dimension, there are not enough degrees of freedom for a system to undergo a phase transition. This is because there is only one direction for particles to move, limiting the complexity and interactions between particles.
A phase transition is a physical change that occurs in a system when a certain set of conditions, such as temperature or pressure, are reached. This change causes the system to transition from one phase or state to another, such as from solid to liquid or liquid to gas.
Yes, phase transition can occur in higher dimensions because there are more degrees of freedom for particles to interact and change their state. This allows for a greater complexity and variety of states that a system can transition between.
There are some exceptions where phase transition can occur in one dimension, such as in certain models of quantum systems. However, these cases are highly specific and do not apply to most physical systems.
Symmetry is an important factor in phase transition as it determines the properties and behavior of a system. In one dimension, there is only one type of symmetry, translational symmetry, which limits the types of phase transitions that can occur. In higher dimensions, there are more types of symmetry that can lead to a wider range of phase transitions.