0$, magnons should be able to propagate in three dimensions. For BEC to occur in quasi-1$D$ system, such as DTN, there must be weak interaction between the 1$D$ chains, which permits full mobility of magnons in 3$D$.

One of the experimental features of the BEC of magnons can be found by analyzing the experimental data at the boundary $H_{c1}(T)$, where part of the excitations condense.

The signature of the BEC universality class at low temperature is given by the power-law [@3; @7; @12; @20; @21; @25; @26] $$H_{c1}(T)-H_{c1}(0) \approx \ A T^{\phi},$$ where $A$ is fully determined by the coefficient of (11) as a function of $v_{0}$ and the mass of magnons.

DTN behaves in 3D below $1.2$ K as a BEC, which is where the long-range order sets in, although the universal behavior with $\phi = 3/2$ is observed only below $T < 0.2$ K. This is because the $\phi = 3/2$ power-law behavior is a low-temperature approximation to the full boson distribution function.

IV. EXPERIMENTAL DETERMINATION OF THE BEC PHASE
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A wealth of useful information about the nature of the transition to the ordered phase can be obtained from several thermodynamics properties in the temperature $vs$. field 