Dynamic Critical Behaviour of φ⁴ Theory

The theory of QCD is expected to have a critical point at the end of the chiral transition line at finite temperature and baryon chemical potential. To ultimately locate this critical endpoint, one will have to find signatures of critical behaviour in collision experiments. However, since collision experiments are of a very dynamic nature, one has to know about the dynamic critical behaviour of QCD to make accurate predictions. An interesting quantity in that respect is the dynamic critical exponent z. The one-component φ⁴ scalar field theory is perfectly suited to test numerical methods on it, since it is very well-known, easy to implement and can be efficiently simulated. Its static critical behaviour is contained in the Ising universality class, whose static critical exponents are known with great precision. Therefore we use it to test a method to calculate the dynamic critical exponent z from first principles. The spectral function of the theory is calculated in the vicinity of the critical point, using a classical statistical approximation. We show that this approximation is valid in the critical regime, where low frequencies dominate. The shape of the spectral function is analyzed to extract an estimate for z by means of finite size scaling methods. The estimate is used to confirm that the critical dynamics of the theory is described by model C in the classification scheme of Halperin and Hohenberg.