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It is widely believed that the critical exponents are the same above and below the critical temperature. At least one experiment was performed in the zero-gravity conditions of an orbiting satellite to minimize pressure differences in the sample. An example of such behavior is the 3D ferromagnetic phase transition.

Some model systems do not obey a power-law behavior. For example, mean field theory predicts a finite discontinuity of the heat capacity at the transition temperature, and the two-dimensional Ising model has a logarithmic divergence.

Murphy – Phase theory

However, these systems are limiting cases and an exception to the rule. Real phase transitions exhibit power-law behavior. Exponents are related by scaling relations, such as.

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It can be shown that there are only two independent exponents, e. It is a remarkable fact that phase transitions arising in different systems often possess the same set of critical exponents. This phenomenon is known as universality. For example, the critical exponents at the liquid—gas critical point have been found to be independent of the chemical composition of the fluid. More impressively, but understandably from above, they are an exact match for the critical exponents of the ferromagnetic phase transition in uniaxial magnets.

Such systems are said to be in the same universality class. Universality is a prediction of the renormalization group theory of phase transitions, which states that the thermodynamic properties of a system near a phase transition depend only on a small number of features, such as dimensionality and symmetry, and are insensitive to the underlying microscopic properties of the system. Again, the divergence of the correlation length is the essential point.

There are also other critical phenomena; e. As a consequence, at a phase transition one may observe critical slowing down or speeding up. The large static universality classes of a continuous phase transition split into smaller dynamic universality classes. In addition to the critical exponents, there are also universal relations for certain static or dynamic functions of the magnetic fields and temperature differences from the critical value.

Another phenomenon which shows phase transitions and critical exponents is percolation. The simplest example is perhaps percolation in a two dimensional square lattice. Sites are randomly occupied with probability p. For small values of p the occupied sites form only small clusters. At a certain threshold p c a giant cluster is formed and we have a second-order phase transition.

Phase transitions play many important roles in biological systems. Examples include the lipid bilayer formation, the coil-globule transition in the process of protein folding and DNA melting , liquid crystal-like transitions in the process of DNA condensation , and cooperative ligand binding to DNA and proteins with the character of phase transition. In biological membranes , gel to liquid crystalline phase transitions play a critical role in physiological functioning of biomembranes.


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In gel phase, due to low fluidity of membrane lipid fatty-acyl chains, membrane proteins have restricted movement and thus are restrained in exercise of their physiological role. Plants depend critically on photosynthesis by chloroplast thylakoid membranes which are exposed cold environmental temperatures.

Thylakoid membranes retain innate fluidity even at relatively low temperatures because of high degree of fatty-acyl disorder allowed by their high content of linolenic acid, carbon chain with 3-double bonds. A simple method for its determination from C NMR line intensities has also been proposed.


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It has been proposed that some biological systems might lie near critical points. Examples include neural networks in the salamander retina, [30] bird flocks [31] gene expression networks in Drosophila, [32] and protein folding. In groups of organisms in stress when approaching critical transitions , correlations tend to increase, while at the same time, fluctuations also increase.

This effect is supported by many experiments and observations of groups of people, mice, trees, and grassy plants. From Wikipedia, the free encyclopedia. See also: Order—disorder. Main article: critical exponent. States of matter.

Cited by other publications

Phase phenomena. Electronic phases. Electronic phenomena. Magnetic phases. Soft matter. Retrieved 10 April Archive for History of Exact Sciences. Blundell Concepts in Thermal Physics. Oxford University Press. Bibcode : PhRvB.. Physical Review B. Physical Review Letters. Bibcode : PhRvL. Bibcode : JNCS.. Wolynes; Wolynes, Peter G. Annual Review of Physical Chemistry. Bibcode : ARPC Bibcode : Sci Bibcode : Natur. The system goes directly from solid to gas a process called sublimation without any intermediate form.

No matter what temperature you choose, either the solid or gas phase will always have lower free energy than the liquid phase. The Clausius-Clapeyron equation can also be written in another form. Suppose the system is on the phase coexistence curve, and is entirely in phase 1.

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Phase Theory

Now consider the thermodynamic process in which we add heat until it has been entirely converted to phase 2 but the temperature has not changed. In this case we are adding a finite amount of energy, so we need to integrate over the process. Fortunately, that is trivial to do. Take another look at Figure There is an arrow at the top of the solid-liquid coexistence curve to indicate it goes on forever. No matter how high you make the pressure, there will always be two distinct phases and a transition between them.

But the liquid-gas transition is another matter. The coexistence curve only goes so far, then comes to an end.

6. Phase Transitions — Introduction to Statistical Mechanics

The point at which it ends is called a critical point. Beyond that point, there are no longer separate liquid and gas phases, just a single phase called a supercritical fluid. To understand why this happens, consider how the liquid and gas phases change as you increase the pressure. The liquid phase is difficult to compress, so pressure changes have little effect on it.

The Kinetic Theory: A Microscopic Description of Matter

The gas phase, on the other hand, is very compressible. As you increase the pressure, its volume decreases steadily. That, of course, means that its entropy decreases too: less volume means fewer possible positions for each molecule. At the same time, its energy also decreases. As the molecules are forced closer together, it becomes easier for them to form hydrogen bonds, so the average number of hydrogen bonds steadily increases.

The upshot is that as you increase the pressure, the free energy difference between the two phases decreases. Eventually it reaches zero, and there is no longer any free energy difference at all. That is what happens at the critical point. To be clear, it is not just that there is no longer a free energy difference.

There is no longer any difference at all between the phases. The essential difference between the solid and liquid can be described by two numbers: the average distance between molecules, and the average number of hydrogen bonds per molecule. In the liquid phase the molecules stay close to each other, held together by hydrogen bonds. In the gas phase, they spread out to fill all available volume. But what if they have no extra volume to fill?