We have precisely investigated the antiferromagnetic phase transition in the ternary rare-earth metal silicide Er5Ir4Si10 single crystal by performing the high-resolution measurement of the low-temperature specific heat under zero-magnetic field and the AC magnetization. In the temperature dependence of important physical quantities associated with the antiferromagnetic phase transition, we have observed anomalies associated with the antiferromagnetic long-range ordering at Neel temperature T-N. We have confirmed that T-N is 3.5 K. In addition, we have first observed two Surprising results. Firstly, a shoulder was observed in the vicinity of 2 K in addition to the sharp peak at T-N corresponding to the antiferromagnetic long-range ordering in the high-resolution measurement of the low-temperature specific heat. Secondly, the anomaly of the AC magnetization at T-N depends on the magnetic field direction. Though we have clearly observed the anomaly of the AC magnetization associated with the antiferromagnetic phase transition at T-N when the AC magnetic field direction is parallel to the c-axis, we have observed no anomaly of the AC magnetization at T-N when the AC magnetic field orientation is perpendicular to the c-axis. These results clarify that our Er5Ir4Si10 single crystal is a quasi-two-dimensional antiferromagnet and then has no magnetic structure of the Er3+ local moments. However, we have observed a peak of the AC magnetization at around 2 K when the AC magnetic field is perpendicular to the c-axis. This temperature corresponds to that at which a shoulder is observed in the high-resolution measurement of the low-temperature specific heat. Furthermore, we have observed no frequency dependence of the AC magnetization which is ordinarily observed in the spin glass state. This result means that there is no disorder in our Er5Ir4Si10 single crystal because the crystal structure of Er5Ir4Si10 has the tetragonal crystal structure in which the octagons of Er3+ ions are stacked. In addition, both the tetragons and the octagons of Er3+ local moments have no magnetic frustration. At last, we can conclude that both the shoulder of the low-temperature specific heat in the vicinity of 2 K and the peak of the AC magnetization at around 2 K, which is only observed when the AC magnetic field direction is perpendicular to the c-axis. correspond to the crystalline electric field effect in the plane which is perpendicular to the c-axis of the tetragonal crystal structure. (C) 2008 Elsevier B.V. All rights reserved.