Phase Transitions and Critical Phenomena

In summary, the conversation discusses the topic of phase transitions and critical phenomena, particularly focusing on renormalization-group transformation and its physical significance. The correlation length critical exponent ν and the length rescaling factor b in relation to the transformation are also mentioned. The conversation concludes by suggesting the use of Wikipedia for further information on the topic.
  • #1
Cryphonus
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Phase Transitions and Critical Phenomena!

First 2 questions are not mathematical questions.So if there is someone who knows about what I am talking about i would be glad to hear what critical phenomena is about, i know i can use google for it and i actually did. But they are not really useful since they use "Encyclopedia Language"...


1. Homework Statement

(a) What is a renormalization-group transformation?
(b) What is the physical significance of a renormalization-group fixed point?
(c) Starting from the relation T’ – TC = λ (T – TC) near the fixed point at TC, derive the
correlation length critical exponent ν occurring in ξ = ξ0 |T-TC| - ν. The length
rescaling factor b of the renormalization-group transformation will occur in your
answer.

2. Homework Equations

relevant equations are give in (c)

3. The Attempt at a Solution
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  • #2


(a) it is a transformation that rexpresses your physical situation in terms of lower energy degrees of freedom but keeping the same physical content. It is related to a change of observation scale (always from microscopic to macroscopic situation, in this sense it is a semi-group)

(b) a fixed point is when your theory decomes scale invariant i.e. when doing RG transformation, it keeps the same properties.

(c) My god ! You know nothing about RG and you want to have your problem solved ? Go to see the wiki page ! Even there you can find the solution !
 

Related to Phase Transitions and Critical Phenomena

1. What is a phase transition?

A phase transition is the physical process in which a substance undergoes a change in its physical state, such as from solid to liquid or from liquid to gas. It occurs when a certain set of conditions, such as temperature or pressure, are reached and the substance's properties change abruptly.

2. What are critical phenomena?

Critical phenomena are the sudden and dramatic changes in a substance's physical properties near a phase transition point. These changes can include the appearance of new physical properties, such as superconductivity or magnetism, and are often accompanied by large fluctuations and long-range correlations.

3. What is the difference between first-order and second-order phase transitions?

In a first-order phase transition, there is a discontinuous change in the substance's physical properties, such as a sudden increase in volume or energy. In contrast, a second-order phase transition involves a continuous change in physical properties, with no sudden jumps or discontinuities.

4. What is the critical point?

The critical point is the specific temperature and pressure at which a substance undergoes a phase transition. At this point, the substance exhibits unique physical properties, such as infinite correlation length and critical exponents, which can be used to study critical phenomena and phase transitions.

5. How are phase transitions and critical phenomena studied?

Scientists use various theoretical models and experimental techniques, such as computer simulations and statistical mechanics, to study phase transitions and critical phenomena. These methods allow researchers to understand the behavior of substances near their critical points and make predictions about their physical properties.

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