Specific heat and ac magnetic susceptibility measurements, spanning low temperatures (T ≥ 40 mK) and high magnetic fields (B ≤ 14 T), have been performed on a two-dimensional (2D) antiferromagnet Cu(tn)Cl2 (tn = C3H10N2). The compound represents an S = 1/2 spatially anisotropic triangular magnet realized by a square lattice with nearest-neighbor (J/kB = 3 K), frustrating nextnearest-neighbor (0 < J ′ /J < 0.6), and interlayer (|J ′′ /J| ≈ 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 ≤ 0.4 K and B ≥ 0 are considered evidence of high degree of 2D magnetic order. In fields lower than the saturation field, Bsat = 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 Bsat 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 Néel ground state, are discussed. PACS numbers: 75.40.-s, 75.10.JmRecently, Cu(tn)Cl 2 has been identified as a potential model system for the realization of the spatially anisotropic triangular lattice from the collinear Néel phase (J ′ /J < 0.6). 15 For Cu(tn)Cl 2 studied in B = 0, no evidence for long-range magnetic order was observed down to 60 mK, and the data suggested intralayer inter-action strengths of J/k B = 3 K and 0 < J ′ /J < 0.6, while the interlayer coupling is |J ′′ /J| ≈ 10 −3 . These interactions are described by the Hamiltonianwhere i, j label intralayer spins and k labels the interlayer ones. J J a b c FIG. 1: Realization of Heisenberg model of a spatially anisotropic triangular lattice within a single bc layer in Cu(tn)Cl2. The layers are stacked along the a direction. The full circles denote Cu 2+ ions.