the onset of magnetic order dominates by two order of magnitudes over that due to the onset of superconductivity.

The zero-field part of the $H-T$ phase diagram of HoNi$_{2}$B$_{2}$C is particularly interesting: superconductivity sets-in at $T_{c}\simeq8$ K. Just below this point, an incommensurate spiral state, $\overrightarrow{k_{c}}\simeq$.92$\overset{\ast}{c}$, develops (see e.g. Refs.[@Lynn-RNi2B2C-mag-xrd; @Canfield-Ho-HT-Diagram; @Canfield-HoNi2B2C-M-Cp]). Furthermore, at $\sim$6.3 K, an additional modulated state with $\overrightarrow{k_{a}}\simeq$0.55$\overset{\ast}{a}$ emerges and around 5 K a deep minimum in $H_{c2}$ develops.[@Canfield-RNi2B2C-Hc2] At $T_{N}=$5 K, an orthorhombic lattice distortion [@Kreyssig-Ho-distortion] sets-in and, concomitantly, both the spiral and the a-axis modulated states are replaced by a commensurate AF structure which coexists with superconductivity down to the lowest measurable temperatures. Generalized susceptibility calculation [@Joo-generalized-susc] related these modulated state to maxima in the exchange coupling transform,$\ J(k)$.

Remarkably, the magnetic ground structures of the heavy and magnetic $R$Ni$_{2}$B$_{2}$C compounds (see Tab.I) are particularly simple: in spite of the manifestation of an orthorhombic distortion and a liquid-helium-temperature magnetic modulation, their ground structures are either an equal-amplitude, AF-type squared-up state (as in $R=$Tm, Er, Tb, Gd) or an equal-amplitude, colinear, commensurate AF state (as in $R=$Ho, Dy). Then, it is of interest to investigate whether the low-temperature thermodynamics of these $R$Ni$_{2}$B$_{2}$C can be described 