  Specific heat and ac magnetic susceptibility measurements, spanning low
temperatures ($T \geq 40$ mK) and high magnetic fields ($B \leq 14$ T), have
been performed on a two-dimensional (2D) antiferromagnet Cu(tn)Cl$_{2}$ (tn =
C$_{3}$H$_{10}$N$_{2}$). The compound represents an $S = 1/2$ spatially
anisotropic triangular magnet realized by a square lattice with
nearest-neighbor ($J/k_{B} = 3$ K), frustrating next-nearest-neighbor ($0 <
J^{\prime}/J < 0.6$), and interlayer ($|J^{\prime \prime}/J| \approx 10^{-3}$)
interactions. The absence of long-range magnetic order down to $T = $ 60 mK in
$B = 0$ and the $T^{2}$ behavior of the specific heat for $T \leq 0.4$ K and $B
\geq 0$ are considered evidence of high degree of 2D magnetic order. In fields
lower than the saturation field, $B_{\text{sat}} = 6.6$ T, a specific heat
anomaly, appearing near 0.8 K, is ascribed to bound vortex-antivortex pairs
stabilized by the applied magnetic field. The resulting magnetic phase diagram
is remarkably consistent with the one predicted for the ideal square lattice,
except that $B_{\text{sat}}$ is shifted to values lower than expected.
Potential explanations for this observation, as well as the possibility of a
Berezinski-Kosterlitz-Thouless (BKT) phase transition in a spatially
anisotropic triangular magnet with the N\'{e}el ground state, are discussed.
