<html><head><meta http-equiv="Content-Type" content="text/html; charset=utf-8"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class="">Arbitrary graphs don’t have a “dimension”. Only lattices do.<br class=""><div><br class=""><blockquote type="cite" class=""><div class="">On 9 Nov 2017, at 14:12, Sun Rongyang <<a href="mailto:sun-rongyang@outlook.com" class="">sun-rongyang@outlook.com</a>> wrote:</div><br class="Apple-interchange-newline"><div class=""><div style="font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; font-family: Calibri, Helvetica, sans-serif; font-size: 12pt;" class="">Dear all,</div><div style="font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; font-family: Calibri, Helvetica, sans-serif; font-size: 12pt;" class=""><br class=""></div><div style="font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; font-family: Calibri, Helvetica, sans-serif; font-size: 12pt;" class="">The definition method of a lattice in ALPS is delicate. But I meet a problem about dimension counting of a pure graph. On the one hand, I define an pure anisotropic graph as:</div><div style="font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; font-family: Calibri, Helvetica, sans-serif; font-size: 12pt;" class=""><br class=""></div><div style="font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; font-family: Calibri, Helvetica, sans-serif; font-size: 12pt;" class="">*************************************************************************************************</div><div style="font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; font-family: Calibri, Helvetica, sans-serif; font-size: 12pt;" class=""><span class=""><div class=""><GRAPH name="anisotropic open ladder graph test"></div><div class=""> <!-- type="0" means horizontal; type="1" means vertical --></div><div class=""> <EDGE tyep="0" source="1" target="2"/></div><div class=""> <EDGE tyep="0" source="2" target="3"/></div><div class=""> <EDGE tyep="0" source="3" target="4"/></div><div class=""> <EDGE tyep="0" source="4" target="5"/></div><div class=""> <EDGE tyep="0" source="6" target="7"/></div><div class=""> <EDGE tyep="0" source="7" target="8"/></div><div class=""> <EDGE tyep="0" source="8" target="9"/></div><div class=""> <EDGE tyep="0" source="9" target="10"/></div><div class=""> <EDGE tyep="1" source="1" target="6"/></div><div class=""> <EDGE tyep="1" source="2" target="7"/></div><div class=""> <EDGE tyep="1" source="3" target="8"/></div><div class=""> <EDGE tyep="1" source="4" target="9"/></div><div class=""> <EDGE tyep="1" source="5" target="10"/></div><div class=""></GRAPH></div><div class=""><span class=""><span style="font-family: Calibri, Helvetica, sans-serif; font-size: 16px; font-style: normal; font-variant-caps: normal;" class="">*************************************************************************************************</span></span><br class=""></div><div class="">On the other hand, I use the default LATTICEGRAPH "open ladder", I copy here:</div><div class=""><br class=""></div><div class=""><span class=""><span style="font-family: Calibri, Helvetica, sans-serif; font-size: 16px; font-style: normal; font-variant-caps: normal;" class="">*************************************************************************************************</span></span><br class=""></div><div class=""><span class=""><div class=""><LATTICE name="square lattice" dimension="2"></div><div class=""> <PARAMETER name="a" default="1"/></div><div class=""> <BASIS><VECTOR>a 0</VECTOR><VECTOR>0 a</VECTOR></BASIS></div><div class=""> <RECIPROCALBASIS><VECTOR>2*pi/a 0</VECTOR><VECTOR>0 2*pi/a</VECTOR></RECIPROCALBASIS></div><div class=""></LATTICE></div></span><br class=""></div><div class=""><span class=""><div class=""><UNITCELL name="anisotropic2d" dimension="2"></div><div class=""> <VERTEX/></div><div class=""> <EDGE type="0"><SOURCE vertex="1" offset="0 0"/><TARGET vertex="1" offset="1 0"/></EDGE></div><div class=""> <EDGE type="1"><SOURCE vertex="1" offset="0 0"/><TARGET vertex="1" offset="0 1"/></EDGE></div><div class=""></UNITCELL></div></span><br class=""></div><div class=""><span class=""><div class=""><LATTICEGRAPH name = "open ladder" vt_name="OpenLadderLattice"></div><div class=""> <FINITELATTICE></div><div class=""> <LATTICE ref="square lattice"/></div><div class=""> <PARAMETER name="W" default="2"/></div><div class=""> <EXTENT dimension="1" size="L"/></div><div class=""> <EXTENT dimension="2" size="W"/></div><div class=""> <BOUNDARY dimension="1" type="open"/></div><div class=""> <BOUNDARY dimension="2" type="open"/></div><div class=""> </FINITELATTICE></div><div class=""> <UNITCELL ref="anisotropic2d"/></div><div class=""></LATTICEGRAPH></div></span><span class=""><span style="font-family: Calibri, Helvetica, sans-serif; font-size: 16px; font-style: normal; font-variant-caps: normal;" class="">*************************************************************************************************</span></span><br class=""></div></span>with parameters L=2, W=5. Will they be treated as the same in ALPS? Or the graph equals as L=5,W=2 open ladder?</div><div style="font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; font-family: Calibri, Helvetica, sans-serif; font-size: 12pt;" class=""><br class=""></div><div style="font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; font-family: Calibri, Helvetica, sans-serif; font-size: 12pt;" class="">Thanks a lot!</div><div style="font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; font-family: Calibri, Helvetica, sans-serif; font-size: 12pt;" class=""><br class=""></div><div style="font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; font-family: Calibri, Helvetica, sans-serif; font-size: 12pt;" class="">Best regards,</div><div style="font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px; font-family: Calibri, Helvetica, sans-serif; font-size: 12pt;" class="">Rongyang Sun</div><div id="signature" style="font-family: Helvetica; font-size: 12px; font-style: normal; font-variant-caps: normal; font-weight: normal; letter-spacing: normal; text-align: start; text-indent: 0px; text-transform: none; white-space: normal; word-spacing: 0px; -webkit-text-stroke-width: 0px;" class=""><div id="divtagdefaultwrapper" dir="ltr" style="font-size: 12pt; font-family: Calibri, Helvetica, sans-serif, Helvetica, EmojiFont, "Apple Color Emoji", "Segoe UI Emoji", NotoColorEmoji, "Segoe UI Symbol", "Android Emoji", EmojiSymbols;" class=""><p style="margin-top: 0px; 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