Dimension, fluctuations, and phase transitions

In summary, Chaikin discusses the effect of fluctuations on different systems and how they can lead to the destruction of ordered states and phase transitions. In one dimension, fluctuations disrupt the flow of information and prevent long-range order and phase transitions, while in two dimensions there are multiple paths for information to travel and maintain order. The lack of order in one dimension makes it impossible to have a phase transition.
  • #1
VortexLattice
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Hey all,

I'm reading Chaikin's Principles of Condensed matter, and he's talking about the effect fluctuations have in various systems. He says:

Below three dimensions, fluctuations become so violent that they can destroy the ordered state and finite temperature phase transitions. In one dimension, fluctuations destroy all long-range order and phase transitions. This is essentially a problem of connectivity. The only way one end of a one-dimensional system knows what is going on at the other end is via information transmitted directly along the chain. For an infinitely long system, any fluctuation cuts the flow of information and hence the order. Since there are always fluctuations at any finite temperature, a one-dimensional system cannot be ordered except at zero temperature. In two-dimensional systems, there are many paths that can connect one part of the system to others.

So I get why order is destroyed in 1D, and not in 2D. But I don't see why they destroy the phase transitions. Can anyone tell me?

Thanks!
 
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  • #2
Well if there is no order, how can you have a phase transition?
 

1. What is meant by "dimension" in science?

In science, dimension refers to the measurable physical quantity that describes the size, extent, or magnitude of an object or phenomenon in space. It can also refer to the number of coordinates needed to locate a point in space.

2. What are fluctuations in science?

Fluctuations in science refer to variations or changes in a physical system or phenomenon over time. These variations can be caused by external factors or internal processes within the system.

3. What are phase transitions in science?

Phase transitions in science refer to the changes in the physical state of a substance or system as it undergoes a change in temperature, pressure, or other external conditions. These changes can result in the transformation of a substance from one state (e.g. solid, liquid, gas) to another.

4. How are dimension, fluctuations, and phase transitions related?

Dimension, fluctuations, and phase transitions are all concepts related to the physical properties and behavior of systems in science. Dimension describes the size and extent of a system, while fluctuations refer to the changes in the system over time. Phase transitions describe the changes in the physical state of a system, which can be affected by fluctuations and the dimension of the system.

5. What are some examples of phase transitions in everyday life?

Examples of phase transitions in everyday life include the melting of ice into liquid water on a hot day, the boiling of water into steam when heated, and the condensation of steam into liquid water when cooled. Other examples include the freezing of liquid into a solid, such as water turning into ice, and the sublimation of dry ice (frozen carbon dioxide) directly into gas without going through a liquid state.

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