simulate this circuit – Schematic created using CircuitLab
Here I have simulated a real Schottky diode (1N5819) and a realistic digital voltmeter (10MΩ input resistance).
Your simulation may also be accurate for the models you are using, however your voltmeter model (at least) is suspect.
Schottky diodes can leak relatively high currents, especially at high temperatures so you should be surprised to see the above 390nA leakage with 1.1V across the diode (reverse bias). Review the Shockley diode equation and a typical diode model (below is Diodes Inc. 1N5819 model, where the saturation current is of particular interest here):
*SRC=1N5819;DI_1N5819;Diodes;Si; 40.0V 1.00A 3.00us Diodes Inc. Schottky Barrier Rectifier
.MODEL DI_1N5819 D ( IS=390n RS=0.115 BV=40.0 IBV=1.00m
+ CJO=203p M=0.333 N=1.70 TT=4.32u )
Spice uses a somewhat more complex set of equations than the Shockley equation to model a diode (there are three regions of operation), but the latter should be adequate for now.