Critical Behaviour
For the critical temperature occurs at absolute zero, resulting in no phase transition for the spherical model. For d greater than 2, the spherical model exhibits the typical ferromagnetic behaviour, with a finite Curie temperature where ferromagnetism ceases. The critical behaviour of the spherical model was derived in the completely general circumstances that the dimension d may be a real non-integer dimension.
The critical exponents and in the zero-field case which dictate the behaviour of the system close to were derived to be
which are independent of the dimension of d when it is greater than four, the dimension being able to take any real value.
Read more about this topic: Spherical Model
Famous quotes containing the words critical and/or behaviour:
“It would be easy ... to regard the whole of world 3 as timeless, as Plato suggested of his world of Forms or Ideas.... I propose a different viewone which, I have found, is surprisingly fruitful. I regard world 3 as being essentially the product of the human mind.... More precisely, I regard the world 3 of problems, theories, and critical arguments as one of the results of the evolution of human language, and as acting back on this evolution.”
—Karl Popper (19021994)
“I cannot be much pleased without an appearance of truth; at least of possibilityI wish the history to be natural though the sentiments are refined; and the characters to be probable, though their behaviour is excelling.”
—Frances Burney (17521840)