Bose-Einstein condensation of magnons

We use the Renormalization Group method to study the Bose-Einstein condensation of the interacting dilute magnons which appears in three dimensional spin systems in magnetic field. The obtained temperature dependence of the critical field Hc(T) – Hc(0) ~ T 2 is different from the recent self-consistent Hartree-FockPopov calculations (cond-matt 0405422) in which a T3/2 dependence was reported. The origin of this difference is discussed in the framework of quantum critical phenomena. Bose-Einstein condensation (BEC) remains one of the most exotic predictions of the quantum mechanics. In the last half-decade a continue interest have been shown with respect to this phenomena because of its experimental evidence in ultra-cooled diluted atomic gases. It is also known that a quantum spin system can be mapped onto an interacting Bose gas. The analogy between a quantum spin system which presents long-range order, and an interacting Bose gas, which presents BEC, is well known for a long time [1]. Recently, these systems became of great interest because the experimental data on the ladder systems showed the possibility of a quantum phase transition (QPT) driven by the magnetic field [2]. A quantum spin liquid is characterized by a finite magnetic correlation length, which is inversely proportional to the energy gap, ∆, between the singlet ground state and the lowest triplet excitation. The effect of a magnetic field on a gapped system is especially interesting for a small gap. Application of on external magnetic field cause a linear reduction of ∆ by the Zeeman effect. The ground state become gapless and the system can undergo 3D magnetic ordering. The existence of the magnetic order in the spin-gap magnetic compounds was predicted by a standard mean-field theory for spins [3]. However, several characteristic features cannot be explained by this theory. For example, the cusp-like minimum of the magnetization as a function of the temperature at the transition, and the power-law like dependence of the critical field () (0) ~ cc HT H T Φ